Question

4 multiple choice 1 point multiply: (3x + 2)(9x^2 - 6x + 4) 27x^3 - 36x^2 + 54x + 8 27x^3 - 36x^2 - 54x + 8 27x^3 + 36x^2 + 54x + 8 27x^3 + 8 5 multiple choice 1 point subtract 4a^2 - 6ab + 3b^2 from b^2 + 6a^2 - 9ab. -2a^2 - 3ab - 2b^2 -2a^2 - 15ab + 4b^2 10a^2 - 15ab + 4b^2 2a^2 - 3ab - 2b^2 6 multiple choice 1 point factor: 4b^2 - 8b - 60 (4b - 10)(b + 6) (2b - 15)(2b + 4) (4b - 20)(b + 3) 4(b - 5)(b + 3)

Explanation:

4.

Step1: Use distributive property

$(3x + 2)(9x^{2}-6x + 4)=3x(9x^{2}-6x + 4)+2(9x^{2}-6x + 4)$

Step2: Multiply each term

$3x(9x^{2}-6x + 4)=27x^{3}-18x^{2}+12x$ and $2(9x^{2}-6x + 4)=18x^{2}-12x + 8$

Step3: Combine like - terms

$(27x^{3}-18x^{2}+12x)+(18x^{2}-12x + 8)=27x^{3}+( - 18x^{2}+18x^{2})+(12x-12x)+8=27x^{3}+8$

Step1: Set up the subtraction

$(b^{2}+6a^{2}-9ab)-(4a^{2}-6ab + 3b^{2})$

Step2: Distribute the negative sign

$b^{2}+6a^{2}-9ab-4a^{2}+6ab - 3b^{2}$

Step3: Combine like - terms

$(6a^{2}-4a^{2})+(-9ab + 6ab)+(b^{2}-3b^{2})=2a^{2}-3ab-2b^{2}$

Step1: Factor out the greatest common factor

First, factor out 4 from $4b^{2}-8b - 60$, we get $4(b^{2}-2b - 15)$

Step2: Factor the quadratic inside the parentheses

We need to find two numbers that multiply to - 15 and add up to - 2. The numbers are - 5 and 3. So $b^{2}-2b - 15=(b - 5)(b + 3)$

Answer:

$27x^{3}+8$

5.