Question

10 multiple choice 1 point simplify: $3a^{2}(7a^{6}+5a^{5}-8a^{4}+1)$ $21a^{8}+15a^{7}-24a^{6}+3a^{2}$ $10a^{8}+8a^{7}-5a^{6}+4a^{2}$ $21a^{12}+15a^{10}-24a^{8}+3$ $10a^{12}+8a^{10}-5a^{8}+4a^{2}$ 11 multiple choice 1 point factor completely: $18x^{2}-63x$ $9(2x^{2}-7x)$ $9x(2x - 7)$ $3x(6x - 21)$ $9x(2x - 8)$ 12 multiple choice 1 point simplify: $(4x^{2}-8xy + 2y^{2})-(9x^{2}-4xy - 7y^{2})$ $-5x^{2}-4xy + 9y^{2}$ $-5x^{2}-12xy + 9y^{2}$ $-5x^{2}-4xy - 5y^{2}$ $-5x^{2}+12xy + 4y^{2}$

Explanation:

Step1: Apply distributive property

$3a^{2}(7a^{6}+5a^{5}-8a^{4}+1)=3a^{2}\times7a^{6}+3a^{2}\times5a^{5}-3a^{2}\times8a^{4}+3a^{2}\times1$

Step2: Use exponent - rule $a^{m}\times a^{n}=a^{m + n}$

$3\times7a^{2 + 6}+3\times5a^{2+5}-3\times8a^{2 + 4}+3a^{2}=21a^{8}+15a^{7}-24a^{6}+3a^{2}$

Step1: Find the greatest common factor (GCF) of $18x^{2}$ and $63x$

The GCF of 18 and 63 is 9, and the GCF of $x^{2}$ and $x$ is $x$. So the GCF of $18x^{2}$ and $63x$ is $9x$.

Step2: Factor out the GCF

$18x^{2}-63x=9x(2x - 7)$

Step1: Distribute the negative sign

$(4x^{2}-8xy + 2y^{2})-(9x^{2}-4xy-7y^{2})=4x^{2}-8xy + 2y^{2}-9x^{2}+4xy + 7y^{2}$

Step2: Combine like - terms

$(4x^{2}-9x^{2})+(-8xy + 4xy)+(2y^{2}+7y^{2})=-5x^{2}-4xy + 9y^{2}$

Answer:

A. $21a^{8}+15a^{7}-24a^{6}+3a^{2}$