Question

I NEED HELP IN 2 QUESTIONS, PLEASE HELP AND SHOW YOUR WORK!

Which expression best represents the area of the rectangle? ( The longer side is x+12, and the shorter side is x-5)

A) x2 + 7x + 60

B) x2 + 17x + 60

C) x2 − 7x + 7

D) x2 + 7x − 60

Multiply: (2x − 5)(3x2 − 4x + 2)

A) 6x3 − 23x2 + 24x − 10
B) 6x3 − 7x2 + 24x − 10
C) 6x3 − 23x2 + 16x − 10
D) 6x3 − 7x2 + 16x − 10

Answer 1

Q1. D) x² + 7x - 60

Q2. A) 6x³³ - 23x² +24x - 10

Explanation:

Q1.

The formula of an area of a rectangle:

`A=l* w`

l - length

w - width

We have l = x + 12 and w = x - 5. Substitute:

`A=(x+12)(x-5)` use FOIL (a + b)(c + d) = ac + ad + bc + bd

`A=(x)(x)+(x)(-5)+(12)(x)+(12)(-5)`

`A=x^2-5x+12x-60` combine like terms

`A=x^2+7x-60`

Q2.

`(2x-5)(3x^2-4x+2)` use the distributive property a(b + c) = ab + ac

`=(2x-5)(3x^2)+(2x-5)(-4x)+(2x-5)(2)\\\\=(2x)(3x^2)+(-5)(3x^2)+(2x)(-4x)+(-5)(-4x)+(2x)(2)+(-5)(2)`

`=6x^3-15x^2-8x^2+20x+4x-10` combine like terms

`=6x^3+(-15x^2-8x^2)+(20x+4x)-10\\\\=6x^3-23x^2+24x-10`