Question

factorise 16x square+8x+1-36y square

Answer 1

Answer:

(4x+6y+1) (4x-6y+1)

Step-by-step explanation:

Refer to the diagram

Hope it helps....

Answer 2

Answer:

$(4x+1+6y)(4x+1-6y)$

Step-by-step explanation:

In the given equation,

$16x^{2}+8x+1-36y^{2}$

To factorise it completely we will have to open up the higher variables and convert them into the smaller ones.

Now,

On further simplifying the equation we get,

$16x^{2}+8x+1-36y^{2}=(4x)^{2}+2(4x)+(1)^{2}-(6y)^{2}\\(4x)^{2}+2(4x)+(1)^{2}-(6y)^{2}=(4x+1)^{2}-(6y)^{2}$

Because,

We have the identities,

We can simplify the above given equation in the simplified form like,

$(a+b)^{2}=a^{2}+b^{2}+2ab\\and,\\a^{2}-b^{2}=(a+b)(a-b)$

We can say that,

$(4x+1)^{2}-(6y)^{2}=(4x+1+6y)(4x+1-6y)$

Therefore, the final factorised form of the equation will be,

$(4x+1+6y)(4x+1-6y)$