Algebraic Expressions and Identities Test - 4

Given: 4xy × 8x²y³z × 2z × ½xyz

4xy × 8x²y³z × 2z × ½xyz = 4 × 8 × 2 × ½ × xy × x²y³z × z × xyz

= 32 × x¹⁺²⁺¹ × y¹⁺³⁺¹ × z¹⁺¹⁺¹

= 32x⁴y⁵z³

Hence, c is the correct answer.

The volume of box = Length × Breadth × Height

= (x – 1) × 2x × 3yz

= (x – 1) × 6xyz

= x × 6xyz – 1 × 6xyz

= 6x²yz – 6xyz

Hence, C is the correct answer

Given expression: s(s – 1)(s + 1) + 2s + s² (s + 1)

s(s – 1)(s + 1) + 2s + s² (s + 1) = (s² – s)(s + 1) + 2s + s³ + s²

= s²(s + 1) – s(s + 1) + 2s + s³ + s²

= s³ + s² – s² – s + 2s + s³ + s²

= 2s³ + s² + s

At s = 3,

= 2 × 27 + 9 + 3

= 54 + 12

= 66

Hence, C is the correct answer.

Expression that contains three terms is called trinomial.

(xy + yz + zx) has three terms, xy, yz and zx.

Hence, D is the correct answer.

An expression that contains two terms is called binomial.

2x + y has two terms as 2x and y.

Hence, C is the correct answer.

Given Expression: x⁷⁵ – x² + 3x⁴⁴ + x – 5x² + 100

We can add the coefficients of x², and we will have,

x⁷⁵ – 6x² + 3x⁴ + x + 100

So, the coefficient of x² is -6.

Hence, C is the correct answer.

To Find: ab – bc + bc – ca + ca – ab

Therefore,

ab – bc + bc – ca + ca – ab = ab – ab + bc – bc + ca – ca

= 0 + 0 + 0

= 0

Hence, D is the correct answer.