Answer:
[tex]4abx^{2}[/tex]
Step-by-step explanation:
we know that
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex] -----> Formula A
and
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex] -----> Formula B
In this problem we have
[tex](ax+bx)^{2}-(ax-bx)^{2}[/tex]
step 1
Solve [tex](ax+bx)^{2}[/tex]
Applying Formula A
[tex](ax+bx)^{2}=(ax)^{2}+2(ab)x^{2}+(bx)^{2}[/tex]
step 2
Solve [tex](ax-bx)^{2}[/tex]
Applying Formula B
[tex](ax+bx)^{2}=(ax)^{2}-2(ab)x^{2}+(bx)^{2}[/tex]
step 3
Substitute
[tex](ax+bx)^{2}-(ax-bx)^{2}=[(ax)^{2}+2(ab)x^{2}+(bx)^{2}]-[(ax)^{2}-2(ab)x^{2}+(bx)^{2}][/tex]
[tex]=(ax)^{2}+2(ab)x^{2}+(bx)^{2}-(ax)^{2}+2(ab)x^{2}-(bx)^{2}[/tex]
[tex]=4abx^{2}[/tex]
