Question

Multiplication using formulas.

Answer 1

Answer:

$4abx^{2}$

Step-by-step explanation:

we know that

$(a+b)^{2}=a^{2}+2ab+b^{2}$ -----> Formula A

and

$(a-b)^{2}=a^{2}-2ab+b^{2}$ -----> Formula B

In this problem we have

$(ax+bx)^{2}-(ax-bx)^{2}$

step 1

Solve $(ax+bx)^{2}$

Applying Formula A

$(ax+bx)^{2}=(ax)^{2}+2(ab)x^{2}+(bx)^{2}$

step 2

Solve $(ax-bx)^{2}$

Applying Formula B

$(ax+bx)^{2}=(ax)^{2}-2(ab)x^{2}+(bx)^{2}$

step 3

Substitute

$(ax+bx)^{2}-(ax-bx)^{2}=[(ax)^{2}+2(ab)x^{2}+(bx)^{2}]-[(ax)^{2}-2(ab)x^{2}+(bx)^{2}]$

$=(ax)^{2}+2(ab)x^{2}+(bx)^{2}-(ax)^{2}+2(ab)x^{2}-(bx)^{2}$

$=4abx^{2}$