Algebraic Expressions and Identities Test - 3

Area of rectangle = length × breadth

= 4ab × 6ab

= 24a²b²

Hence, D is the correct answer.

We know that, (a + b) (a – b) = a² – b²

101 × 99 = (100 + 1) (100 – 1)

= (100)² – (1)²

= 10000 – 1

= 9999

Hence, B is the correct answer.

Given: (x – 2) (x + 2) (x² + 4) (x⁴ + 16)

We know that, (a + b) (a – b) = a² – b²

So,

(x – 2) (x + 2) (x² + 4) (x⁴ + 16) = (x² – 4) (x² + 4) (x⁴ + 16)

= (x⁴ – 16) (x⁴ + 16)

= x⁸ – 256

Hence, B is the correct answer.

We know that, (a - b)² = a² + b² - 2ab

(4)² = a² + b² – 2 × 2

a² + b² = 16 + 4

= 20

Hence, D is the correct answer.

(7x + y) × (x + 7y) = 7x × (x + 7y) + y × (x + 7y)

= 7x² + 49xy + xy + 7y²

= 7x² + 7y² + 50xy

Hence, A is the correct answer.

(x – 5)(x + 5) + 25 = x × (x + 5) – 5 × (x + 5) + 25

= x² + 5x – 5x – 25 + 25

= x²

Hence, B is the correct answer.

(a + b)(a – b) + (a² + b²) = a × (a – b) + b × (a – b) + (a² + b²)

= a² – ab + ab – b² + (a² + b²)

= 2a²

Hence, C is the correct answer.

(a + b)(c – d) = a × (c – d) + b × (c – d)

= ac – ad + bc – bd

(a – b)(c + d) = a × (c + d) – b × (c + d)

= ac + ad – bc – bd

(a + b) (c – d) + (a – b) (c + d) = ac – ad + bc – bd + ac + ad – bc – bd

= 2ac – 2bd

(a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd) = 2ac – 2bd + 2ac + 2bd

= 4ac

Hence, C is the correct answer.