Question

The product of (7a-8b) and (7a-8b) is
(A) 14m^2-112ab+16b^2
(B) 49a^2+112ab-64b^2
(C) 49a^2-112ab+64b^2
(D) 49a^2-112ab-64b^2​

Answer 1

Required Answer:

$\bf{ \bullet \: Given: -}$

Two expression -

1. 7a - 8b
2. 7a - 8b

$\bf{ \bullet \: Options: -}$

a. 4a² - 112ab + 16b²

b. 49a² + 112ab - 64b²

c. 49a² - 112ab + 64b²

d. 49a² - 112ab - 64b²

$\bf{ \bullet \: What \: To \: Find: -}$

We have to find the product of the two expressions.

$\bf{ \bullet \: How \: To \: Find: -}$

Method 1 -

Use the distributive property.

Method 2 -

Use the identity, (a - b) (a - b) = (a - b)² = (a² - 2ab + b²).

$\bf{ \bullet \: Solution: -}$

Method 1 -

(7a - 8b) × (7a - 8b)

Use distributive property,

⇒ 7a(7a-8b) - 8b(7a-8b)

Multiply each term,

⇒ (7a × 7a - 7a × 8b) - (8b × 7a - 8b × 8b)

Solve the brackets,

⇒ 49a² - 56ab - 56ab - 64b²

Solve the like term,

⇒ 49a² - 112ab - 64b²

Method 2 -

(7a - 8b) × (7a - 8b)

Also written as,

⇒ (7a - 8b)²

Use the identity,

⇒ $\overline{\boxed{ (a - b)^2 = a^2 - 2ab + b^2}}$

Substitute the value,

⇒ 7a² - 2(7a × 8b) + 8b²

Solve the value,

⇒ 49a² - 156ab + 64b²

$\tt{ \therefore Thus, the \: product \: is \: 4a^2 - 112ab + 64b^2 \: ie \: Option \: C.}$