Algebra 1 Multiplication of Polynomials

Simplify the expressions below. Write the final product in standard form and show your work.

2x^4(4x^2 + 3x + 1)
(4x – 3)(2x^2 – 7x + 1)
(x^2 + 4x – 3)(2x^2 + x + 6)
Write a simplified polynomial expression to represent the area of the rectangle below.

(To the right of the rectangle, there is x+5, and at the bottom of the rectangle, there is 2x-4.)

Write a simplified polynomial expression to represent the area of the square tile, shown below.

(At the bottom of a square, there is x-3)

sol'n:

Rule:
(x^a)(x^b) = x^(a+b)

so..

1.)
(2x^4)(4x^2 + 3x + 1)

= 8x^(4+2) + 6x(^4+1) + 2x^4

= 8x^6 + 6x^5 + 2x^4

2.) (4x – 3)(2x^2 – 7x + 1)

= 8x^(1+2) - 28x^(1+1) - 4x - 6x^2 + 21x - 3

= 8x^3 - 28x^2 - 4x - 6x^2 + 21x - 3

= 8x^3 - 34x^2 - 17x - 3

3.) (x^2 + 4x – 3)(2x^2 + x + 6)

= 2x^4 + x^3 + 6x^2
+ 8x^3 + 4x^2 + 24x
- 6x^2 - 3x - 18

Then combine like terms.

= 2x^4 + 9x^3 + 4x^2 + 21x - 18