Question

Please help

Factor completely (4 points each):

-9x^4+1296

3x^6-1029y^9

5a^5b^10+60a^3b^5x^2+180ax^4

9x^2y^2-27x^2y-72y^2+216y

Answer 1

9[12 - x²][12 + x²]

-3[-x² + 7y³][x⁴ + 7y³x² + 49y⁶]

5a[a²b⁵ + 6x²]²

9y[3 - y[8 - x²]

Explanation:

Factor out the Greatest Common Factor [GCF], meaning that some terms in the order they are have to have those exact same terms along with the least degree term possible, and for the coefficients, they have to be divisible by some sort.

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Answer 2

1.
`-9 (x^2 - 12) (x^2 + 12)`

2.
`3\left(x^2-7y^3\right)\left(x^4+7x^2y^3+49y^6\right)`

3.
`5a\left(a^2b^(5)+6x^2\right)^2`

4.
`9y\left(y-3\right)\left(x^2-8\right)`

Explanation:

1.

The given expression is

`-9x^4+1296`

Taking out GCF,

`-9(x^4-144)`

`-9((x^2)^2-(12)^2)`

`-9(x^2 - 12) (x^2 + 12)`
`[\because a^2-b^2=(a-b)(a+b)]`

2.

The given expression is

`3x^6-1029y^9`

Taking out GCF,

`3(x^6-343y^9)`

`3((x^2)^3-(7y^3)^3)`

`3\left(x^2-7y^3\right)\left(x^4+7x^2y^3+7^2y^6\right)`
`[\because a^3-b^3=(a-b)(a^2+ab+b^2)]`

`3\left(x^2-7y^3\right)\left(x^4+7x^2y^3+49y^6\right)`

3.

`5a^5b^(10)+60a^3b^5x^2+180ax^4`

Rewrite the above expression.

`5aa^4b^(10)+12\cdot \:5aa^2b^5x^2+36\cdot \:5ax^4`

Taking out GCF,

`5a\left(a^4b^(10)+12a^2b^5x^2+36x^4\right)`

`5a\left((a^2b^(5))^2+2(6a^2b^5)x^2+(6x^2)^2\right)`

`5a\left(a^2b^(5)+6x^2\right)^2`
`[\because (a+b)^2=a^2+2ab+b^2]`

4.

`9x^2y^2-27x^2y-72y^2+216y`

Rewrite the above expression.

`9x^2yy+3\cdot \:9x^2y+8\cdot \:9yy+24\cdot \:9y`

Taking out GCF,

`9y\left(x^2y-3x^2-8y+24\right)`

`9y\left((x^2y-3x^2)+(-8y+24)\right)`

`9y\left(x^2(y-3)-8(y-3)\right)`

`9y\left(y-3\right)\left(x^2-8\right)`