Maharashtra Board Class 7 Maths part 1 Chapter 8 Algebraic Expressions and Operations on them PDF Download

Algebraic Expressions And Operations On Them

Let's Learn: Algebraic Expressions

Look at the arrangements of sticks given below and observe the pattern.

On observing the pattern above, we notice that Number of sticks = 3 × number of squares + 1.

Here, the number of squares changes. It could be any of the numbers 2, 3, 4, ... , 10, ... If we do not know the number of squares, we write a letter in its place. Here, the number of squares is shown by the letter n.

'n' is a variable. \(3n + 1\) which is the same as \(3n + 1\) is an algebraic expression in the variable n.

Three balls = 3 balls

Three triangles = 3 triangles

\(t + t + t = 3t\)'s

Balls + Bats = Balls + Bats

Mangoes + Guavas = Mangoes + Guavas

\(x + x + y + y + y = 2x + 3y\)

Perimeter of a rectangle = \(2l + 2b = 2(l + b)\)

Now I Know!

\(3n + 1\), \(3t\), \(2x + 3y\), \(2(l + b)\) are algebraic expressions.

n, t, y, l, b, x are the variables in these expressions.

Teacher's Note

Algebraic expressions help us write patterns in a short way. Like when we count sticks in a pattern, we use letters instead of writing the number every time. This is just like using variables in real life, such as using 'x' for any number of students in a class.

Exam Trick

Remember: A variable is always a letter like n, x, y, t. The number written before the letter is the coefficient. For example, in 3n, the 3 is the coefficient of n.

Points to Remember

An algebraic expression uses letters called variables to show changing numbers.

A coefficient is the number written before a variable.

We can write patterns with algebraic expressions to save time.

Different letters represent different quantities.

Algebraic expressions make math easier and faster.

Example

In the algebraic expression \(4x^2 - 2y + \frac{5}{6}xz\):

\(4x^2\) is the first term and 4 is the coefficient in it.

\(-2y\) is the second term with the coefficient -2.

\(\frac{5}{6}xz\) is the third term and \(\frac{5}{6}\) is the coefficient in it.

Let's Learn

In the expression \(3x\), 3 is the coefficient of the variable x.

In the expression \(-t\), -1 is the coefficient of the variable t.

An expression in which multiplication is the only operation is called a 'term'.

An algebraic expression may have one term or may be the sum of several terms.

Remember:

The algebraic expression \(15 - x\) has two terms. The first term is 15 which is a number. The second term is \(-x\). Here, the coefficient of the variable x is (-1).

Terms which have the same variables with the same powers are called 'like terms'.

Like terms: (i) \(2x\), \(5x\), \(-\frac{2}{3}x\) (ii) \(-5x^2y\), \(\frac{6}{7}yx^2\)

Unlike terms: (i) \(xy\), \(y^2\) (ii) \(-2xyz\) (iii) \(mn\), \(m^2n^2\), \(m^3n\)

Types Of Algebraic Expressions

Expressions are named after the number of terms they have. Expressions with one term are called monomials, those with two terms binomials, with three terms trinomials and if they have more than three terms, they are called polynomials.

Teacher's Note

Monomials have one term, binomials have two terms, and trinomials have three terms. It's like sorting fruits - mangoes only, mangoes with apples, or mangoes with apples and bananas all together.

Exam Trick

Remember: Count the number of terms separated by + or - signs. If there is 1 term it is monomial, 2 terms = binomial, 3 terms = trinomial, and more than 3 = polynomial.

Points to Remember

Monomials have only one term with no + or - between parts.

Binomials have exactly two terms separated by + or -.

Trinomials have exactly three terms.

Polynomials have four or more terms.

Always count the terms carefully by looking at + and - signs.

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