Question

Hello, I need help with factoring quadratics:
64a2 - 48a + 9
I only know how to factor ones with no coefficient, please help!

Answer 1

You could look at it like:

\[64(a^2-\frac{48}{64}a+\frac{9}{64})\] and solve that one in parenthesis then multiply it by 64 afterwards.

Answer 2

Hint
24 + 24 = 48
24*24 = 576

Answer 3

64a^2 - (24 + 24)a + 9
64a^2 -24a - 24a + 9

Answer 4

8a(8a - 3) -3(8a - 3)

@OceanBEAUTI16 are you following?

Answer 5

So how are you getting the eight?

Answer 6

64a^2 - 24a = 8a(8a - 3)

-24a + 9 = -3(8a - 3)

By factoring out the GCF of each set of binomials.

Answer 7

Thanks! How about this one, since it doesn't have a middle term. 16n^2 - 49

Answer 8

For that use the difference of squares rule:

\[a^2 - b^2 = (a + b)(a - b)\]

Answer 9

So that's what it means, thank you :)

Answer 10

these all are special quadratics, u should memorize below identities :

\(\large (a+b)^2 = a^2+2ab + b^2\)

\(\large (a-b)^2 = a^2-2ab + b^2\)

\(\large a^2-b^2 = a^2-b^2\)

Answer 11

In this case
a = 4n
b = 7

And
a^2 = (4n)^2 = 16n^2
b^2 = (7)^2 = 49

Answer 12

I love squares, they're so much easier.

Answer 13

64a^2 - 48a + 9 = (8a - 3)^2

Which is also a square

Answer 14

Right! Sometimes things just go over my head *ahem*. Thanks!