Question

fctorize 72a^2 - 2 ( b - c ) ^2​

Answer 1

Answer:

$\large\boxed{2(36a^2-b^2+2bc-c^2)}$

Step-by-step explanation:

To solve this problem, first you have to find the factors of 72a²-2(b-c)² from left to right. Also, you had to use distributive property or perfect square.

Given:

72a²-2(b-c)²

Solution:

First, you have to use perfect square to solve with distributive property from left to right.

$\large\boxed{\textnormal{Perfect Square Formula}}$

$\displaystyle (a-b)^2=a^2-2ab+b^2$

A=B

B=C

$\displaystyle b^2-2bc+c^2$

$\displaystyle 72a^2-2(b^2-2bc+c^2)$

Next, expand to solve with distributive property.

$\large\boxed{\textnormal{Distributive property}}$

$\displaystyle a(b+c)=ab+ac$

$\displaystyle -2(b^2-2bc+c^2)=-2b^2+4bc-2c^2$

$\displaystyle-2b^2+4bc-2c^2=72a^2-2b^2+4bc-2c^2$

Then, rewrite the problem.

$\displaystyle 2*36a^2-2b^2+2*2bc-2c^2$

Solve.

$\displaystyle 2*36a^2-2b^2+2*2bc-2c^2=\boxed{2(36a^2-b^2+2bc-c^2)}$

$\large\boxed{2(36a^2-b^2+2bc-c^2)}$

So, the correct answer is 2(36a²-b²+2bc-c²).