Binomial Products Review G8

Name the Polynomial(s) and give the highest degree

100

4y + 7

Binomial and a first degree polynomial

200

3x³

Monomial and third degree polynomial

300

4x² + 5x + 6

Trinomial and a second degree polynomial

400

7

Monomial and a zero degree polynomial

500

9x ⁴ + 24x² + 16x -15

Polynomial and a fourth degree polynomial

Distributive Principle

100

4(3x + 4)

12x + 16

200

2(5x + 6)

10x + 12

300

6(x+12)

6x+72

400

-3(2x-6)

-6x+18

500

4x(3x-y+5)

12x²-4xy+20x

Adding or Subtracting Polynomials

100

(3x+5) + (4x+1)

7x + 6

200

(6x-7) + (4x+5)

10x-2

300

(5x-7) - (8x-2)

-3x - 5

400

(5x-3) + (4x+7) + (2x-6)

11x-2

500

(6x-8) - (6x+8)

-16

Multiplying Binomials

100

(x+2)(x+3)

x² + 3x + 2x + 6 = x²+5x+6

200

(x-7)(x+2)

x² + 2x - 7x - 14 = x²-5x-14

300

(2x+4)(x-8)

2x² - 16x + 4x - 32 = 2x²-12x-32

400

(x-4)²

(x-4)(x-4) = x² - 4x - 4x = 16x²-8x+16

500

What does the FOIL means?

First term, Outer term, Inner term, and Last term.

Special Products of Binomials

100

(2x - 3)²

4x² - 12x + 9

200

(2x + 3)(2x - 3) =

4x² -9

300

What is the coefficient of xy in the product (5x - 3y)² ?

The coefficient of xy in the product is -2(5)(3) = -30.

400

A square swimming pool has a side length of (x - 2) feet. The swimming pool is surrounded by a square walkway which its side length is (x + 1) feet. Write and simplify an expression for the area of the walkway.

(x+1)² - (x-2)² = (x²+2x+1)-(x²-4x+4) = 6x-3

500

Explain the Error.

Marco wrote the expression (2x - 7y)² = 4x² - 49y² . Explain and correct his error.

He wrote the difference of the squares of the terms instead of square of a binomial difference. 

The correct product is 4x² - 28xy + 49y².