Question

50 POINTS!!! Plz show work questions are in the addon

Answer 1

1. Each term in this polynomial has a common factor of $3x^3$:

$12x^6-9x^4+18x^3=3x^3(4x^3-3x+6)$

2. Not sure what the "vertical method" is, but I would guess it refers to some way of visualizing the distributive property.

$(3x-5)(2x^2+7x-3)=3x(2x^2+7x-3)-5(2x^2+7x-3)$

$(3x-5)(2x^2+7x-3)=(6x^3+21x^2-9x)+(-10x^2-35x+15)$

$(3x-5)(2x^2+7x-3)=6x^3+11x^2-44x+15$

3. You can use the same approach as in (2), or recall that $(a+b)^2=a^2+2ab+b^2$:

$(5x-4y)^2=(5x)^2+2(5x)(-4y)+(-4y)^2$

$(5x-4y)^2=25x^2-40xy+16y^2$

4. Recall that a difference of squares can be factored as $a^2-b^2=(a-b)(a+b)$. So

$(2x^2-7)(2x^2+7)=(2x^2)^2-7^2$

$(2x^2-7)(2x^2+7)=4x^4-49$