Question

how to factor 9x^2-16

Answer 1

this is difference of 2 squares

use the identity a^2 - b^2 = (a + b)(a - b)

Answer 2

its confusing me because the x^2 is part of the nine

Answer 3

a^2 is equavalent to 9x^2 so
a -------------- 3x
right?

Answer 4

yes

Answer 5

and b^2 equivalent to 16
b …………………………..?

Answer 6

4

Answer 7

To factor a difference of two squares you need to recognize that the exponents of all the powers in it are even and the numerical coefficient is the square of an integer.

Answer 8

right so plug those values into RHS of the identity

Answer 9

so its 3^2-4^2?

Answer 10

$$\huge 9x^2-16=(3x)^2-4^2$$

Answer 11

no just plug in a = 3x and b = 4 into (a + b)(a - b)

Answer 12

Oh i get it so its (3x+4)(3x-4)

Answer 13

yes

Answer 14

Correct :)

Answer 15

but what if its x^3+27? how would I go about solving that?

Answer 16

That is a sum of cubes.

Answer 17

do i do (x2+9)(x+3)

Answer 18

just look out for difference of 2 perfect squares
eg

x^ 2 - 9

16y^2 - 25

Answer 19

$$\huge x^3+27=x^3+3^3$$

Answer 20

for the second equation the answer is (4y-5)(4y+5) :)

Answer 21

skullpatrol how do i put that in the equation cwrw was showing me?

Answer 22

It requires a different identity.

Answer 23

what is that identity?

Answer 24

$$\huge x^3+y^3=(x+y)(x^2-xy+y^2)$$

Answer 25

how do i plug it in then?

Answer 26

$$\huge x^3+3^3$$

Answer 27

do i have to put it in ( ) ( ) that form or can i just leave my answer as x^3+3^3

Answer 28

You have to put it in ( ) ( ) form.

Answer 29

how do i do that? im sorry im very slow especially when it comes to math :/

Answer 30

Use the identity with x = x and y = 3.

Answer 31

so it'll look like (x+3)(x^2-x3+3^2) ?

Answer 32

yes

Answer 33

but that makes no sense

Answer 34

why

Answer 35

because if yo solve it it doesnt come out to be x^3+3^3

Answer 36

its okay I'll just ask my teacher tomorrow Im probably frustrating you now thanks for the help though!