Question

Factor the expression a^2-6ab+9b^2 into a product of binomials

Answer 1

Hint: Find two numbers that multiply to 9 and add to -6

Answer 2

Lets's take b to be a constant and rewrite the expression as: a^2-(6b)a+9b^2
We need to first two numbers whose: (1) sum is -6b{middle term} (2) product is 1*9b^2 {products of first term and coefficient of first term}
These two numbers are....as you guessed it: -3b and -3b.
Replace -6ab in the equation with these two numbers:
a^2-3ab-3ab+9b^2
Now group them like: (a^2-3ab)+(-3ab+9b^2)
Factor out common stuff from both bracketed terms and complete the question.

Answer 3

Oh, sorry @jim_thompson5910 , did too much of the question :)

Answer 4

that's ok, your explanation is a good one allank

Answer 5

Thanks jim.

Answer 6

np

Answer 7

thanks i got
a^2 -6ab+9b^3
a^2-3ab-3ab+9b^2
a(a-3b)-3b(a-3b)
(a-3b)(a-3b)
is this right?

Answer 8

that is correct

Answer 9

you can also write it as (a-3b)^2

Answer 10

okay thank you

Answer 11

yw