CBSE Class 7 Mathematics Algebraic Expressions Assignment Set 06

Question 1. Classify the following as monomials, binomials and trinomials
(i) \( 4x^2 - 5 \)
(ii) \( 3x^2 - 5x + 6 \)
(iii) \( \frac{3}{5}xyz \)
(iv) \( 4x^3 + 3x^2 - 6 \)
(v) \( 5x^3 - 6 \)
Answer:
(i) Binomial (it has two unlike terms: \( 4x^2 \) and \( -5 \))
(ii) Trinomial (it has three unlike terms: \( 3x^2 \), \( -5x \), and \( 6 \))
(iii) Monomial (it has only one term: \( \frac{3}{5}xyz \))
(iv) Trinomial (it has three unlike terms: \( 4x^3 \), \( 3x^2 \), and \( -6 \))
(v) Binomial (it has two unlike terms: \( 5x^3 \) and \( -6 \))
In simple words: Count how many parts are separated by plus or minus signs. One term is a monomial, two terms make a binomial, and three terms make a trinomial.
Exam Tip: Make sure terms cannot be added together before counting them. Only count terms that are unlike.

Question 2. Write the degree of the following algebraic expression (in \( x \) only)
(i) \( 4x^2y + x^4 + 6x^6 \)
(ii) \( \frac{3}{7}x^3y - 5x^3y^3 + 7x^7 \)
(iii) \( \frac{5}{7}xy - 6 \)
(iv) \( 5xy + x^3 - x^2 \)
Answer:
(i) The powers of \( x \) are 2, 4, and 6. The greatest power is 6, so the degree in \( x \) is 6.
(ii) The powers of \( x \) are 3, 3, and 7. The largest power is 7, so the degree in \( x \) is 7.
(iii) The variable \( x \) appears with a power of 1, so the degree in \( x \) is 1.
(iv) The powers of \( x \) are 1, 3, and 2. The greatest power is 3, so the degree in \( x \) is 3.
In simple words: Look only at the letter x. Find the biggest exponent on x in any of the terms.

Exam Tip: Read carefully when a question says "in x only". Do not add the powers of other variables like y in this case.

Question 3. Write the following into algebraic language
(i) \( x \) cube minus two times \( x \) square
(ii) Five subtracted from \( x \) square
(iii) Age of father is twice the age of his son.
Answer:
(i) \( x^3 - 2x^2 \)
(ii) \( x^2 - 5 \)
(iii) Let the son's age be \( x \) years and the father's age be \( y \) years. Then, the statement gives: \( y = 2x \)
In simple words: Turn the word description into math symbols. Put minus signs, powers, and letters where the words say.

Exam Tip: In phrases like "five subtracted from \( x^2 \)", remember that the number after "from" comes first: \( x^2 - 5 \), not \( 5 - x^2 \).

Question 4. Write the co-efficient of \( x \) in
(i) \( 2x - 3y \)
(ii) \( 5xy^2 - 5y^3 \)
(iii) \( \frac{3}{7}xy^3 + \frac{2}{7}y^4 \)
Answer:
(i) The term containing \( x \) is \( 2x \). Removing \( x \) leaves 2. Thus, the coefficient of \( x \) is 2.
(ii) The term containing \( x \) is \( 5xy^2 \). Leaving out \( x \) gives \( 5y^2 \). Thus, the coefficient of \( x \) is \( 5y^2 \).
(iii) The term containing \( x \) is \( \frac{3}{7}xy^3 \). Leaving out \( x \) gives \( \frac{3}{7}y^3 \). Thus, the coefficient of \( x \) is \( \frac{3}{7}y^3 \).
In simple words: Find the term that has x in it. Take away x, and everything left in that term is its coefficient.

Exam Tip: A coefficient can include numbers as well as other variables. Include the full multiplying factor attached to x.

Question 5. Write the co-efficient of
(i) \( p^2 \) in \( \frac{12}{5}p^2 \)
(ii) \( x^3 \) in \( 4x^3 - 3x + 5 \)
(iii) \( x \) in \( -4x + \frac{9}{13} \)
(iv) \( q \) in \( -\frac{4}{3}p^2r^2q + \frac{9}{5} \)
Answer:
(i) In \( \frac{12}{5}p^2 \), the factor with \( p^2 \) is \( \frac{12}{5} \).
(ii) In \( 4x^3 - 3x + 5 \), the factor with \( x^3 \) is 4.
(iii) In \( -4x + \frac{9}{13} \), the factor multiplying \( x \) is \( -4 \).
(iv) In the term \( -\frac{4}{3}p^2r^2q \), removing \( q \) leaves \( -\frac{4}{3}p^2r^2 \).
In simple words: Look at the term that has the given letter. The remaining part of that term is the coefficient.

Exam Tip: Always keep the minus sign with the coefficient if the term is negative, such as \( -4 \) or \( -\frac{4}{3}p^2r^2 \).

Question 6. Identify the constant term in the following
(i) \( 4x^2y - 7 + p^2x \)
(ii) \( \frac{3}{7}xy - \frac{4}{5}x + \frac{9}{7} \)
(iii) \( 3p^2x + 4q^2y \)
(iv) \( \frac{3}{5}p^2x^2 - \frac{5}{6}px + \frac{9}{5} \)
Answer:
(i) The term with no variables is \( -7 \).
(ii) The term without any variables is \( \frac{9}{7} \).
(iii) Every term contains a variable, so the constant term is 0.
(iv) The term containing only numbers is \( \frac{9}{5} \).
In simple words: A constant term is just a number that has no letters attached to it.

Exam Tip: If all terms in an expression have variables, the constant term is 0. Do not leave the answer blank.

Question 7. Write the factors of the following monomials
(i) \( 3x^2yz \)
(ii) \( -\frac{5}{9}xyz \)
(iii) \( \frac{3}{4}x^2y^2z^2 \)
(iv) \( 7x^2ypq \)
Answer:
(i) The factors of \( 3x^2yz \) are \( 3, x, x, y, z \). (Written as \( 3 \times x \times x \times y \times z \))
(ii) The factors of \( -\frac{5}{9}xyz \) are \( -\frac{5}{9}, x, y, z \). (Written as \( -\frac{5}{9} \times x \times y \times z \))
(iii) The factors of \( \frac{3}{4}x^2y^2z^2 \) are \( \frac{3}{4}, x, x, y, y, z, z \). (Written as \( \frac{3}{4} \times x \times x \times y \times y \times z \times z \))
(iv) The factors of \( 7x^2ypq \) are \( 7, x, x, y, p, q \). (Written as \( 7 \times x \times x \times y \times p \times q \))
In simple words: Split the term into every single number and letter that multiply together to make it.

Exam Tip: Expand powers fully into individual factors, such as writing \( x^2 \) as \( x \times x \).

Question 8. Identify the terms and represent in the form of tree diagram.
(i) \( 4x^2y + 6xy^2 \)
(ii) \( 3abc + 4p^2q^2 \)
Answer:
(i) The terms of the expression are \( 4x^2y \) and \( 6xy^2 \).
The factors of \( 4x^2y \) are \( 4, x, x, y \).
The factors of \( 6xy^2 \) are \( 6, x, y, y \).
Tree diagram:
(ii) The terms of the expression are \( 3abc \) and \( 4p^2q^2 \).
The factors of \( 3abc \) are \( 3, a, b, c \).
The factors of \( 4p^2q^2 \) are \( 4, p, p, q, q \).
Tree diagram:
In simple words: Put the full expression at the top. Branch down to each term, and then branch down from each term to its factors.

Exam Tip: The top level is the expression, the middle level shows the terms, and the bottom level shows the irreducible factors.

Question 9. State whether each pair of terms given below is like or unlike.
(i) \( 4x^2y \) and \( 4xy^2 \)
(ii) \( 3x^2y^2z^2 \) and \( 6x^2y^2z^2 \)
(iii) \( 3xy^2 \) and \( \frac{5}{3}x^2y \)
(iv) \( 5pq \) and \( 7p^2q^2r \)
Answer:
(i) Unlike (the powers of \( x \) and \( y \) differ between the two terms)
(ii) Like (both terms have the exact same variables with the same powers: \( x^2y^2z^2 \))
(iii) Unlike (the exponents of the variables do not match)
(iv) Unlike (the variables and their exponents are not the same)
In simple words: Terms are like if they have the exact same letters with the exact same powers. If not, they are unlike.

Exam Tip: Numerical coefficients do not have to be the same for terms to be like terms; only the variable parts and their exponents must match.

Question 10. Identify the like terms in the following algebraic expressions.
(i) \( 5x^2 - 3xy + 3x^2 - 1 \)
(ii) \( 4xy - 4x^2y^2 - 2xy - 2x^2y^2 + 9xy \)
(iii) \( x^2 - 2y^2 + 7x^2 - 9y^2 - 2xy + xy \)
Answer:
(i) Like terms are: \( 5x^2 \) and \( 3x^2 \)
(ii) Like terms are: \( 4xy, -2xy \), and \( 9xy \); also \( -4x^2y^2 \) and \( -2x^2y^2 \)
(iii) Like terms are: \( x^2 \) and \( 7x^2 \); \( -2y^2 \) and \( -9y^2 \); also \( -2xy \) and \( xy \)
In simple words: Group together the terms that share the exact same combination of letters and powers.

Exam Tip: Remember to include the positive or negative sign with each like term when listing them.