which of the following is equivalent to, (3x–4y)(3x+4y)?

A. 9x^2 + 16y^2
B. 9x^2 – 16y^2
C. 9x^2 – 24xy – 16y^2
D. 6x^2 – 14xy + 16y^2
E. 6x^2 – 8y^2

Respuesta :

Hello!

The answer is:

B. [tex]9x^{2}-16y^{2}[/tex]

Why?

To find the equivalent expression we need to apply the distributive property, so:

[tex](3x-4y)(3x+4y)=9x^{2}+12xy-12yx-16y^{2}\\\\9x^{2}+12xy-12yx-16y^{2}=9x^{2}+12xy-12xy-16y^{2}=9x^{2}-16y^{2}[/tex]

So, the correct option will be B. [tex]9x^{2}-16y^{2}[/tex]

Have a nice day!