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(a) x – 3

(b) \( 1 + x + x^2\)

(c) \( y – y^3\)

(d)\( 5xy^2 + 7x^2y \)

(e) \(-ab + 2b^2 – 3a^2 \)

Answer :

(a) Expression: ( x-3 )

Term I = x

Term II = -3

(b) Expression: \( 1 + x + x^2\)

Term I = 1

Term II = x

Term III = \( x^2 \) = x × x

(c) Expression: \( y – y^3\)

Term I = y

Term II = \( -y^3 \) = -y × -y ×-y

(d) Expression: \( 5xy^2 + 7x^2y \)

Term I = \(5xy^2 \) = 5×x×y×y

Term II = \( 7x^2y \) = 7× x × x × y

(e) Expression: \(-ab + 2b^2 – 3a^2 \)

Term I = -ab = -a × b

Term II = \( 2b^2 \) = 2 × b × b

Term III = \( -3a^2 \) = -3 ×a×a

- Q.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 number m and n. (vii) Product of numbers y and z subtracted from 10. (viii) Sum of numbers a and b subtracted from their product.
- Q.2 (ii) Identify terms and factors in the expression given below: (a) -4x + 5 (b) -4x + 5y (c) \(5y + 3y^2\) (d)\( xy + 2x^2y^2 \) (e) pq + q (f) 1.2ab – 2.4b + 3.6a (g) \(\frac{3}{4} x+\frac{1}{4} \) (h) \( 0.1p^2 + 0.2q^2 \)
- Q.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) \( – p^2q^2 + 7pq \) (vi)\( 1.2 a + 0.8 b \) (vii)\( 3.14 r^2 \) (viii)\( 2 (l + b) \) (ix)\( 0.1 y + 0.01 y^2 \)
- Q.4 (a) Identify terms which contain x and give the coefficient of x. (i)\( y^2x + y\) (ii) \( 13y^2 – 8yx\) (iii) \( x + y + 2\) (iv)\( 5 + z + zx \) (v) \( 1 + x + xy \) (vi)\( 12 xy^2 + 25 \) (vii) \( 7x + xy^2 \)
- Q.4 (b) Identify terms which contain \( y^2 \)and give the coefficients of\( y^2.\) (i) \( 8 – xy^2 \) (ii) \( 5y^2 + 7x \) (iii) \(2x^2y – 15xy^2 + 7y^2 \)
- Q.5 Classify into monomials, binomials and trinomials: (i) 4y – 7x (ii)\( y^2 \) (iii) x + y – xy (iv) 100 (v) ab – a – b (vi) 5 – 3t (vii) \( 4p^2q – 4pq^2 \) (viii) 7mn (ix)\( z^2 – 3z + 8 \) (x) \( a^2 + b^2 \) (xi)\( z^2 + z \) (xii) \(1 + x + x^2 \)
- Q.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)\( 4m^2p, 4mp^2 \) (vi) \(12xz, 12 x^2y^2 \)
- Q.7 Identify like terms in the following: \( (a)-xy^2, -4yx^2, 8x^2, 2xy^2, 7y^2, -11x^2,\) \( -100x, -11yx, 20x^2y, -6x^2, y, 2xy, 3x \) \( (b) 10pq, 7p, 8q, -p^2q^2, -7qp, -100q, -23, 12q^2p^2, \) \( -5p^2, 41, 2405p, 78qp, 13p^2q, qp^2, 701p^2 \)

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