How do you factor 49x^2-144?

2 Answers
May 14, 2018

(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: 7x*7x=49x^2
Secondly, multiply the outer numbers/vars.: 7x*-12=-84x
Thirdly, multiply the inner numbers/vars.: 7x*12=84x
Lastly, multiply the last numbers/vars.:12*12=144
The two number, 84x and 84x, cancel themselves out and leaves one with 49x-144
One CAN'T use this perfect square method IF the equation has a plus instead of a minus.

May 14, 2018

(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)