Question

Please help

Answer 1

Answer:

9[12 - x²][12 + x²]

-3[-x² + 7y³][x⁴ + 7y³x² + 49y⁶]

5a[a²b⁵ + 6x²]²

9y[3 - y[8 - x²]

Step-by-step 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

Answer:

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

Step-by-step 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,

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

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

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

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