Question

Factorise $a^2-81(b-c{)}^2$

• A. 5y + 2y + y - 7y = y
• B. (a+ 9b- 9c)(a-9b-9c)
• C. (a+ 9b+9c)(a-9b-9c)
• D. (a-b+c)(a-b-c)

Answer 1

The correct option is B

(a+ 9b- 9c)(a-9b-9c)

Given : $a^2-81(b-c{)}^2$
= $a^2-\left(9\right(b-c){)}^2$

We know that,

$(a^2-b^2)$ = $(a+b)(a-b)$

Using the above formula we can write,

$(a-9(b-c\left)\right)(a+9(b-c\left)\right)$
= $(a-9b+9c)(a+9b-9c)$