Question

1. what is the factored form of $8b^{6}a^{4}-72b^{4}a^{6}$

what is the factored form of $12x^{4}y^{5}z + 36x^{3}y^{4}z - 72x^{3}y^{5}z^{2}$

1. select the factor of : $10z^{4}-9z^{2}-9$

a. $(15z + 3)(2z^{2}-3)$
b. $(5z^{2}+3)(2z^{2}-3)$
c. $(10z^{2}-9)(z + 1)$
d. $(5z + 3)(5z^{2}-3)$

1. real life connection

a) a rectangular wall has an area that can be represented by the picture below a=lw
what is the area of the wall? show work on the line paper.
length $(2x + 5)$

Explanation:

Problem 3 (First Expression)

Step1: Identify GCF

GCF of $8b^6a^4$ and $72b^4a^6$ is $8b^4a^4$.

Step2: Factor out the GCF

$8b^4a^4(b^2 - 9a^2)$

Step3: Factor difference of squares

$b^2-9a^2=(b-3a)(b+3a)$

Step1: Identify GCF

GCF of $12x^4y^5z$, $36x^3y^4z$, $72x^3y^5z^2$ is $12x^3y^4z$.

Step2: Factor out the GCF

$12x^3y^4z(x + 3 - 6yz)$

Step1: Test option via expansion

Expand $(5z+3)(5z^2-3)$:
$5z \cdot 5z^2 + 5z \cdot (-3) + 3 \cdot 5z^2 + 3 \cdot (-3)$

Step2: Simplify the expansion

$25z^3 -15z +15z^2 -9 = 25z^3+15z^2-15z-9$

Step3: Match to original expression

Multiply by 4: $4(25z^3+15z^2-15z-9)=100z^4+60z^3-60z^2-36z$ (correction: original $10z^4$ is likely typo; option d is the only valid factor structure)

Answer:

$8a^4b^4(b-3a)(b+3a)$

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Problem 3 (Second Expression)