CBSE Class 7 Mathematics Algebraic Expression Worksheet Set 01

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Question. What is the number of diagonals that can be drawn from one vertex in a heptagon.
Answer : 4

Question. What should be added into x² + x + a to obtain x² + x – 3?
Answer : –3 – a

Question. Add the unlike terms : 8x, (-4/3) x, (2/3) y, 3p
Answer : (2/3 y+3P)

Question. Evaluate : 2a² + 3b² + 1c² if a = 1, b = 0, c = –4
Answer : 18

Question. What is the numerical coefficient of algebraic expression 13 – y².
Answer : –1

Question. Each ......... consists of 4 line segments. Find the total number of line-segments in the following figure ........... :
Answer : 16

Question. Add the algebraic expression :
(i) 7x – 4 and 3x + 1
(ii) Find the coefficient of x.
Answer : 10x – 3, 10

Question. Find the value of (a – b) (a + b) – (2a – b) (a + b) if a = 3, b = 2.
Answer : (–15)

Question. If a = 3, b = –3, find the value of a² + b².
Answer : 18

Question. If a = 5, b = –5, find the value of a² – b².
Answer : 0

Question. Simplify the following expression if x = 8
5x + 6(x – 3)
Answer : 70

Question. What should be subtracted from 3a + 7b – 16 to get 2a + 8b?
Answer : (+ a – b – 16)

Question. What is the coefficient of y in the term (3/4) x²yz² ?
Answer : (4/3) x² z²

Question. Side of a square is 2x cm. Find its area.
Answer : 4x² cm²

Question. Add a² + b² + c² – 3abc and a² – b² + c² + abc.
Answer : 2a² + 2c² – 2abc

Question. What is the number of diagonals that can be drawn from one vertex in an octagon?
Answer : 5

Question. If a = 2 find the value of a(1+1/a)
Answer : 3

Question. Simplify : 5a - {3a - (2 - a) + 4}
Answer : a – 2

Question. By how much is a² – 7a + 5 less than 3a² + 2a + 5?
Answer : 2a² + 9a

Question. Subtract 1 – 5y² from y³ + 7y² + y + 1.
Answer : y³ + 12y² + y

Question. Add the expressions 7a - 5ab + 4b, – 6a - ab - 8b and - 4a + 2ab + 3b.
Answer : –3a – 4ab – b

Question. Subtract x² - 3xy + 7y² - 5 from 6xy - 4x² - y² + 5
Answer : 9xy – 5x² – 8y² + 10

Question. Add all the terms : 12x, 12, 25x, – 25y, 1, x, 12y, y, –25
Answer : –12x – 12y – 12

Question. Base of a triangle is 2x units and its height is 3y units. Find the area of the triangle
Answer : 3xy square units

Question. By how much is 2x³ + 7x² – 5x + 6 greater than x³ – 2x² + x + 5?
Answer : x³ + 9x² – 6x + 1

I Fill in the blanks :

Question a. \(4xy + 2xy\) is a __________________ (bionomial, trinomial, monomial)
Answer: monomial
In simple words: Like terms can be added together to form a single term. Here, \(4xy + 2xy = 6xy\), which has only one term.

Exam Tip: Always simplify expressions containing like terms before classifying them into monomials, binomials, or trinomials.

Question b. The product of twice of 'a' and thrice of 'b' _________________
Answer: \(6ab\)
In simple words: Twice of 'a' is \(2a\) and thrice of 'b' is \(3b\). Their product is \(2a \times 3b = 6ab\).

Exam Tip: Product means multiplication. Multiply the numerical coefficients together and the variables together.

Question c. The constant term of \(12 + 19a^3b^2\) is _________________
Answer: 12
In simple words: A constant term is a fixed number that does not contain any variables.

Question d. The like terms of \(a^2b, -b^2a, -5ba^2, 5ab, 3a^3b, 4ab^3\) are __________
Answer: \(a^2b, -5ba^2\) (and depending on variable order interpretation, \(-b^2a\) and \(5ab\))
In simple words: Like terms have the exact same variable parts with the same exponents, regardless of the order of multiplication.

Exam Tip: Remember that \(a^2b\) and \(ba^2\) are like terms because of the commutative property of multiplication.

Question e. The value which satisfies an equation is called its _______________
Answer: root (or solution)
In simple words: The number that makes the left side equal to the right side when substituted into the equation.

Exam Tip: The terms 'solution of an equation' and 'root of an equation' are used interchangeably.

Question f. Algebraic terms that have the same algebraic factors are called _______________.
Answer: like terms
In simple words: Terms with identical variable components are known as like terms.

Exam Tip: Only like terms can be added or subtracted together.

Question g. The numerical factor of a term is called _______________.
Answer: coefficient
In simple words: The number multiplied by the variables in a term is its coefficient.

Exam Tip: If no number is visible before a variable, the numerical coefficient is understood to be 1.

Question h. A _______________ is product of factors.
Answer: term
In simple words: An algebraic term is formed by the product of numbers and variables.

Exam Tip: Terms are separated by plus (+) or minus (-) signs in an algebraic expression.

Question i. Any expression with one or more terms is called a _______________.
Answer: polynomial
In simple words: An expression consisting of one or more terms with non-negative integer exponents is a polynomial.

Exam Tip: Monomials, binomials, and trinomials are all special types of polynomials.

Question j. A combination of constants and variables connected by the signs of the fundamental operations is called ____________
Answer: algebraic expression
In simple words: Numbers and letters joined by addition, subtraction, multiplication, or division form an algebraic expression.

Exam Tip: Fundamental operations refer to addition, subtraction, multiplication, and division.

II.

Question a. (p - q) - (p + q) = _______________
Answer: \(-2q\)
Opening the brackets:
\(= p - q - p - q\)
Grouping like terms:
\(= (p - p) + (-q - q) = -2q\)
In simple words: Subtracting both terms inside the second parenthesis changes their signs, allowing positive and negative p to cancel out.

Exam Tip: Always distribute the negative sign carefully to every term inside the parentheses when subtracting an expression.

Question b. _______________ should be subtracted from \(3x^3 - 1\) to get \(x^3\)
Answer: \(2x^3 - 1\)
Let the required expression be \(A\).
According to the question:
\((3x^3 - 1) - A = x^3\)
\(A = (3x^3 - 1) - x^3\)
\(A = 2x^3 - 1\)
In simple words: Subtract the target result from the original expression to find what was taken away.

Exam Tip: To find what must be subtracted from expression P to get Q, calculate \(P - Q\).

Question c. The sum of \(-4pqr, 5pqr\) and \(7pqr\) is _______________
Answer: \(8pqr\)
Adding the like terms:
\(= -4pqr + 5pqr + 7pqr\)
\(= (-4 + 5 + 7)pqr\)
\(= 8pqr\)
In simple words: Combine the numerical coefficients of the like terms while keeping the variables unchanged.

Exam Tip: When adding like terms, only add their coefficients.

Question d. The (x + 2) + (x - 2) = _______________
Answer: \(2x\)
Opening brackets and grouping like terms:
\(= x + 2 + x - 2\)
\(= (x + x) + (2 - 2)\)
\(= 2x\)
In simple words: The constant terms \(+2\) and \(-2\) cancel each other out, leaving \(2x\).

Exam Tip: Grouping like terms makes simplification quick and error-free.

III

Question a. Find the sum of \(2x^2 - 3y^2, 9x^2 + 6y^2, -3x^2 - 5y^2\)
Answer: \(8x^2 - 2y^2\)
Writing the sum of all expressions:
\(= (2x^2 - 3y^2) + (9x^2 + 6y^2) + (-3x^2 - 5y^2)\)
Grouping like terms together:
\(= (2x^2 + 9x^2 - 3x^2) + (-3y^2 + 6y^2 - 5y^2)\)
Simplifying coefficients:
\(= 8x^2 - 2y^2\)
In simple words: Group all \(x^2\) terms together and all \(y^2\) terms together, then add their numbers.

Exam Tip: Rearrange terms by degree and variable type before performing addition.

Question b. Subtract \((a^2 + b^2 + 2ab)\) from \((a^2 + b^2 - 2ab)\)
Answer: \(-4ab\)
Setting up the subtraction:
\(= (a^2 + b^2 - 2ab) - (a^2 + b^2 + 2ab)\)
Opening brackets and changing signs:
\(= a^2 + b^2 - 2ab - a^2 - b^2 - 2ab\)
Grouping like terms:
\(= (a^2 - a^2) + (b^2 - b^2) + (-2ab - 2ab)\)
\(= 0 + 0 - 4ab\)
\(= -4ab\)
In simple words: Subtracting an expression means changing the sign of every term inside that expression.

Exam Tip: Pay close attention to the phrasing "Subtract A from B", which means write it as \(B - A\).

Question c. Write the term containing \(a^2\) and find its coefficient
i) \(16a^2 - 4b^2 + 10\)
ii) \(22b^2 - a^2\)
Answer:
i) Term containing \(a^2\) is \(16a^2\); Coefficient of \(a^2\) = 16
ii) Term containing \(a^2\) is \(-a^2\); Coefficient of \(a^2\) = -1
In simple words: Identify the part of the expression that has \(a^2\) and write down the number multiplying it.

Exam Tip: Remember that a negative sign in front of a variable term implies a coefficient of -1.

Question d. Simplify \(2(x^2 + 2xy) + 5 - xy - y^2\)
Answer: \(2x^2 + 3xy - y^2 + 5\)
Distributing 2 into the bracket:
\(= 2x^2 + 4xy + 5 - xy - y^2\)
Grouping like terms (\(4xy\) and \(-xy\)):
\(= 2x^2 + (4xy - xy) - y^2 + 5\)
\(= 2x^2 + 3xy - y^2 + 5\)
In simple words: Expand the bracket first using multiplication, then combine any like terms.

Exam Tip: Use the distributive law \(a(b + c) = ab + ac\) to clear parentheses before combining like terms.

Question e. Find the value of the given expressions when \(a = 0, b = -1, c = 1\)
i) \(a^3 - b^3\)
ii) \(a^2 + 2ab + b^3\)
iii) \(3ab + 3ac + c^2\)
iv) \(-4b\)
Answer:
i) For \(a^3 - b^3\):
Substitute \(a = 0\) and \(b = -1\):
\(= (0)^3 - (-1)^3\)
\(= 0 - (-1) = 0 + 1 = 1\)

ii) For \(a^2 + 2ab + b^3\):
Substitute \(a = 0\) and \(b = -1\):
\(= (0)^2 + 2(0)(-1) + (-1)^3\)
\(= 0 + 0 + (-1) = -1\)

iii) For \(3ab + 3ac + c^2\):
Substitute \(a = 0, b = -1, c = 1\):
\(= 3(0)(-1) + 3(0)(1) + (1)^2\)
\(= 0 + 0 + 1 = 1\)

iv) For \(-4b\):
Substitute \(b = -1\):
\(= -4(-1) = 4\)
In simple words: Replace each variable with its given numerical value and compute the arithmetic result using standard order of operations.

Exam Tip: Use parentheses around negative numbers when substituting values to avoid sign errors, especially with exponents.