Exponent Rules and Polynomials

Exponent Rules

100

Use the product rule for exponents to multiply:

4x^3*5x^2

20x^5

200

3x^2(7x+5)

21x^3+15x^2

300

Use the power rule to simplify:

(4x^2yz^3)^2

16x^4y^2z^6

400

(4x^2y)(-5xy^2)

-20x^3y^3

500

Use the exponent rules to simplify:

(x^3y^4)^3*(3xy^2)^2

9x^11y^16

Adding & Subtracting Polynomials

100

Add the following polynomials. Write your final answer in standard form.

(4x^2+4)+(19x^2-7)

23x^2-3

200

Add the following polynomials. Write your final answer in standard form.

(13x^2y-2x+1)+(9x^2y-7)

22x^2y-2x-6

300

Add the following polynomials. Write your final answer in standard form.

(-x^3+8x^2-5)+(10x^3-x^2+1)

9x^3+7x^2-4

400

Subtract the following polynomials. Write your final answer in standard form.

(3x+2)-(11x-6)

-8x+8

500

Subtract the following polynomials. Write your final answer in standard form.

(x^2-x+4)-(x^2+x-2)

-2x+6

Multiplying Polynomials (mixed)

100

Multiply the polynomials. Write your final answer in standard form.

-3x(2x^2+4)

-6x^3-12x

200

Multiply the polynomials. Write your final answer in standard form.

(9x+1)(6x+2)

54x^2+24x+2

300

Multiply the polynomials. Write your final answer in standard form.

(4x-1)^2

16x^2-8x+1

400

Multiply the polynomials. Write your final answer in standard form.

(2x-5)(3x^2-x+6)

6x^3-17x^2+17x-30

500

(3x^2+2)(2x^2-5x+1)

(6x^4-15x^3+7x^2-10x+2)

Binomial*binomial

100

(3v+7)(v+4)

3v²+19v+28

200

(5x+4)(5x-4)

25x²-16

300

(5a-4)(2a+3)

10a²+7a-12

400

(5a²-b)(5a²+b)

25b² - b²

500

(8b-6a)²

64b²-96ab+36a²

Binomial*Trinomial

100

(5k+4)(k²-8k+5)

5k³-36k²-7k+20

200

(r-1)(6r²-3r+5)

6r³-9r²+8r-5

300

(4m+7)(4m²+4m-4)

16m³+44m²+12m-28

400

(4k-1)(k²-8k+1)

4k³-33k²+12k-1

500

(6x+3y)(6x²-2xy-8y²)

36x³+6x²y-54xy²-24y³