Question

factorise x square - 1 - 6y- 9y square

Answer 1

x^2-[1^2+2(1)(3y^2) +3y^2] x^2 - (1+3y)^2 (x+1+3y)(x-1-3y)

Answer 2

Answer: The factored form of the given expression is $(x-3y-1)(x+3y+1)$.

Explanation:

The given expression is,

$x^2-1-6y-9y^2$

Take out the common negative sign from the last three terms.

$x^2-(1+6y+9y^2)$

It is also written as,

$x^2-(1^2+2(1)(3y)+(3y)^2)$

Using the formula $a^2+2ab+b^2=(a+b)^2$, we get,

$x^2-(1+3y)^2)$

Now using the formula $a^2-b^2=(a+b)(a-b)$, we get,

$[x-(1+3y)][x+(1+3y)]$

$(x-1-3y)(x+1+3y)$

Therefore, $(x-1-3y)(x+1+3y)$ is the factor form of the given expression.