## MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

Question 1.

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y.

(ii) One-half of the sum of numbers x and y.

(iii) The number z multiplied by itself.

(iv) One-fourth of the product of numbers p and Q.

(v) Numbers x and y both squared and added.

(vi) Number 5 added to three times the product of numbers m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

Solution:

(i) y – z

(ii) \(\frac{1}{2}\)(x + y)

(iii) z^{2}

(iv) \(\frac{1}{4}\)(pq)

(v) x^{2} + y^{2}

(vi) 5 + 3 (mn)

(viii) ab – (a + b)

Question 2.

(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

(a) x – 3

(b) 1 + x + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) -ab + 2b^{2} – 3a^{2}

(ii) Identify terms and factors in the expressions given below:

(a) -4x + 5

(b) -4x + 5y

(c) 5y + 3y^{2}

(d) xy + 2x^{2}y^{2}

(e) pq + q

(f) 1.2ab – 2.4b + 3.6a

(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\)

(h) 0.1p^{2} + 0.2q^{2}

Solution:

(i)

Question 3.

Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t^{2}

(ii) 1 + t + t^{2} + t^{3}

(iii) x + 2xy + 3y

(iv) 100m + 1000n

(v) -p^{2}q^{2} + 7pq

(vi) 1.2a + 0.8b

(vii) 3.14 r^{2}

(viii) 2(l + b)

(ix) 0.1y + 0.01y^{2}

Solution:

Question 4.

(a) Identify terms which contains x and give the coefficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x + xy

(vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

(b) identify terms which contains y^{2} and give the coefficient of y^{2}.

(i) 8 – xy^{2}

(ii) 5y^{2} + 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

(a)

Question 5.

Classify into trinomials.

(i) 4y – 7z

(ii) y^{2}

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p^{2}q – 4pq^{2}

(viii) 7mn

(ix) z^{2} – 3z + 8

(x) a^{2} + b^{2}

(xi) z^{2} + z

(xii) 1 + x + x^{2}

Solution:

The monomials, binomials and trinomials have 1, 2 and 3 unlike terms in it respectively.

(i) 4y – 7z Binomial

(ii) y^{2} Monomial

(iii) x + y – xy Trinomial

(iv) 100 Monomial

(v) ab – a – b Trinomial

(vi) 5 – 3t Binomial

(vii) 4p^{2}q – 4pq^{2} Binomial

(viii) 7mn Monomial

(ix) z^{2} – 3z + 8 Trinomial

(x) a^{2} + b^{2} Binomial

(xi) z^{2} + z Binomial

(xii) 1 + x + x^{2} Trinomial

Question 6.

State whether a given pair of terms is of like or unlike terms.

(i) 1,100

(ii) -7x, \(\frac{5}{2}\)x

(iii) -29x, -29y

(iv) 14xy, 42yx

(v) 4m^{2}p, 4mp^{2}

(vi) 12xz, 12x^{2}z^{2}

Solution:

The terms which have same algebraic factors are called like terms. However, when terms have different algebraic factors, these are called unlike terms.

(i) 1,100 Like

(ii) -7x, \(\frac{5}{2}\)x Like

(iii) -29x, -29y Unlike

(iv) 14xy, 42yx Like

(v) 4m^{2}p, 4mp^{2} Unlike

(vi) 12xz, 12x^{2}z^{2} Unlike

Question 7.

Identify like terms in the following:

(a) -xy^{2}, -4yx^{2}, 8x^{2}, 2xy^{2}, 7y, -11x^{2}, -100x, -11yx, 20x^{2}y, -6x^{2}, y, 2xy, 3x

(b) 10pg, 7p, 8q, -p^{2}q^{2}, -7qp, – 100q, -23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}g, qp^{2},701p^{2}

Solution:

(a) -xy^{2} and 2xy^{2}; -4yx^{2} and 20x^{2}y; 8x^{2}, -11x^{2} and -6x^{2}; 7y and y, -100x and 3x; -11yx and 2xy

(b) 10pq, -7qp and 78qp; 7p and 2405p; 8q and -100y; -p^{2}q^{2} and 12q^{2}p^{2}, -23 and 41; -5p^{2} and 701 p^{2}; 13p2^{2}q and qp^{2}