Question

Factorise ${\left(3-4y-7y^2\right)}^2-{\left(4y+1\right)}^2$

• A. $\left(7y^2-4\right)\left(7y^2-8y-2\right)$
• B. $\left(4-7y^2\right)\left(2-8y-7y^2\right)$
• C. $\left(7y^2-4\right)\left(2-8y-7y^2\right)$
• D. $\left(4-7y^2\right)\left(7y^2+8y-2\right)$

Answer 1

The correct option is B $\left(4-7y^2\right)\left(2-8y-7y^2\right)$

We have,

${\left(3-4y-7y^2\right)}^2-{\left(4y+1\right)}^2$

We know that

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

Therefore,

$\Rightarrow (3-4y-7y^2+4y+1)(3-4y-7y^2-4y-1)$

$\Rightarrow (4-7y^2)(2-8y-7y^2)$

Hence, this is the answer.