Question

Multiplication using formulas.

Expand and simplify the following:

(ax + by)^2 - (ax - by)^2 =


Can you please explain

Answer 1

`4abx^(2)`

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)`