# Math Problems?

Factor 64 - 9y^2

Show how please

### 11 Answers

- Φ² = Φ+1Lv 710 months ago
64 - 9y²

= 8² - (3y)²

= 8² + 0 - (3y)²

= 8² + (8×3y - 8×3y) - (3y)²

= 8² + 24y - 24y - (3y)²

= 8(8 + 3y) - 3y(8 + 3y)

= (8 - 3y)(8 + 3y)

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- oubaasLv 710 months ago
it is the difference of 2 squares ( 64 = 8^2 ; 9y^2 = (3y)^2 ) ...and you are supposed to know that a^2-b^2 = (a+b)*(a-b)...therefore :

64 - 9y^2 = (8+3y)*(8-3y)

- DavidLv 410 months ago
This is a standard factorisation rule that can be useful to remember, the difference of two squares:

a² - b² = (a + b)(a - b).

If you multiply out the bracket, the cross terms cancel.

So if you have something of the form ax² - b for some constants a and b, you know that you can factor them into

ax² - b = (√ax + √b)(√ax - √b)

In this case, both factors are perfect squares, so it works particularly nicely:

64 - 9y² = (8 + 3y)(8 - 3y)

- PuzzlingLv 710 months ago
Learn to recognize the difference of squares and how to factor it:

a² - b² = (a + b)(a - b)

In your case:

a² = 64

b² = 9y²

So:

a = 8

b = 3y

Answer:

(8 + 3y)(8 - 3y)