How do you factor 49x^2-144?

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: 7$x \cdot$7$x$=49${x}^{2}$
Secondly, multiply the outer numbers/vars.: 7$x \cdot$-12=-84$x$
Thirdly, multiply the inner numbers/vars.: 7$x \cdot$12=84$x$
Lastly, multiply the last numbers/vars.:12$\cdot$12=144
The two number, 84$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.

May 14, 2018

${\left(7 x\right)}^{2} - {12}^{2} = \left(7 x + 12\right) \left(7 - 12\right)$

Explanation:

Factor:

$49 {x}^{2} - 144$

This is a difference of squares. Use the formula:

$\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$,

where:

$a = 7 x$ and $b = 12$

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

${\left(7 x\right)}^{2} - {12}^{2} = \left(7 x + 12\right) \left(7 - 12\right)$