Question

Factor 49x^2-7^2
and please explain how

Answer 1

`49x^2-7^2=49(x-1)(x+1)`

Explanation:

Factoring

We need to recall this property of binomials:

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

It allows us to factor the difference between two squares as follows.

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

The given expression is

`49x^2-7^2`

Comparing with the above expression:

`a^2=49x^2`

Taking square root:

`a = 7x`

`b^2=7^2`

Taking square root:

b=7

Factoring:

`49x^2-7^2=(7x-7)(7x+7)`

Now we can see each factor can be taken out the common factor 7:

`49x^2-7^2=7(x-1)*7(x+1)`

Multiplying:

`\boxed{49x^2-7^2=49(x-1)(x+1)}`