factor completely: 9a^2 -24ab + 16b^2?

Answer 1

First: break each set apart to find the the least common factor: in this case, we don't have a common factor:

3(3)aa - 2(2)(2)(3)ab + 2(2)(2)(2)bb

Second: take the first coefficient and multiply it by the last coefficient = 144. Find two numbers that give you 144 when multiplied and -24 (middle coefficient) when added/subtracted.

*We can use: -12, -12

Third: rewrite as: (9a^2-12ab) - (12ab+16b^2) and factor.

3a(3a - 4b) - 4b(3a - 4b)

Fourth: combine the outer terms with one inner term:

= (3a - 4b)(3a - 4b)

Answer 2

Both will be (#a - #b) because the second number is negative and the third is positive.
so now we have this ( a - b ) ( a - b ) = 9a^2 - 24ab + 16b^2
now try combinations to get the a's to multiply out to 9
(those combinations are 1x9 and 3x3)
lets use the 3's (because thats the right one)
(3a - b) (3a - b) = 9a^2 - 24ab + 16b^2
now you do the same thing with the b's
(cominations are 1x16, 2x8, 4x4)
lets use the 4's (because thats the right one)
so now you have (3a - 4b)^2
and thats your answer
remember you can always check by FOILing
and then you'll end up with the 9a^2 - 24ab + 16b^2

Answer 3

= 9a^2 -24ab + 16b^2
= (3a)^2 - 24ab + (4b)^2

24= 2 x 3 x 4

so use that (a+b)^2 formula

(3a-4b)^2

Answer 4

This is a perfect square: (3a -4)^2

Answer 5

9a² -24ab + 16b²
(3a - 4b)(3a -4b)
::

Answer 6

a^2 - 24ab - 25b^2 First discover elements of - 25b^2 with opposite indicators. Then upload one yet another. verify which elements supply 24 by technique of including the values with opposite indicators. - 25b^2 = -25b * b and it supplies by technique of including, -25b+b = -24b So the elements are -25 and a million a^2 - 24ab - 25b^2 = (a - 25b)*(a+b)

Answer 7

(3a-4b)(3a-4b)

Check:
9a^2-12ab-12ab+16b^2=
9a^2-24ab+16b^2

Answer 8

(3a-4b)^2

Answer 9

(3a-4b)^2

Answer 10

(3a-4b)(3a-4b) = (3a-4b)^2