81a^2 - (3a + b)^2?

Question

how do i do this

Answer 1

I assume you want to simplify this?

(3a+b)^2 = (3a+b)(3a+b) =
3a(3a+b) + b(3a+b) =
9a^2 + 3ab + 3ab + b^2 =
9a^2 + 6ab + b^2
(in general, (x+y)^2 = x^2 + 2xy + y^2)

So 81a^2-(3a+b)^2 =
81a^2 - 9a^2 - 6ab - b^2 =
72a^2 - 6ab - b^2

Answer 2

I HAVE A BETTER ANSWER FOR THAT. SAME ONE AS THE OTHER ONE BUT WITH A LITTLE DIFFERENCE. ANYWAYS, I'LL DO IT AS WELL.

81a^2-[(3a)^2+2(3a)(b)+(b)^2]
81a^2-(9a^2+6ab+b^2)
81a^2-9a^2-6ab-b^2
72a^2-6ab-b^2
(12a+b)(6a-b) -----> try it on

Answer 3

In order to simplify this, first notice that the expression you gave is a difference of squares.

81a^2 - (3a +b)^2 = (9a + (3a + b))(9a - (3a + b))
Now simplify within each parenthesis
= (9a + 3a + b)(9a -3a -b)
= (12a + b)(6a -b)

And that is about as simple as it will look.

Answer 4

81a^2 - (3a + b)^2
=81 a^2 -9a^2-6ab-b^2
=72a^2-6ab-b^2
= (12a + b)(6a -b)