Question

How do you factor `49x^2-144`?

Answer 1

(7x+12)(7x-12)

Explanation:

This problem is known as a 'perfect square.' The square root of 49 is 7 and the square root of `x^2` is `x`. The next number, 144, is also a perfect square and the answer to that is 12.
Firstly, multiply the first numbers/variables: 7`x*`7`x`=49`x^2`
Secondly, multiply the outer numbers/vars.: 7`x*`-12=-84`x`
Thirdly, multiply the inner numbers/vars.: 7`x*`12=84`x`
Lastly, multiply the last numbers/vars.:12`*`12=144
The two number, 84`x` and 84`x`, cancel themselves out and leaves one with 49`x`-144
One CAN'T use this perfect square method IF the equation has a plus instead of a minus.

Answer 2

`(7x)^2-12^2=(7x+12)(7-12)`

Explanation:

Factor:

`49x^2-144`

This is a difference of squares. Use the formula:

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

where:

`a=7x` and `b=12`

Plug in the known values for `a` and `b`.

`(7x)^2-12^2=(7x+12)(7-12)`