POLYNOMIALS

Addition

100

(4 + 2n ³ ) + (5n ³ + 2)

Simpify:(4 + 2n ³ ) + (5n ³ + 2) 

Step 1: 2n³+5n³+4+2

Combine like terms

Answer: 7n³+6

200

 (4x⁴ – 7x² + 4) + (3x³ – 4x² – 7)

Simpify:(4x⁴ – 7x² + 4) + (3x³ – 4x² – 7)

Step 1: 4x⁴+3x³ – 7x²  – 4x² + 4 – 7

Combine like terms: 4x²    -7x²+4

                              +   3x³-4x²-7

Answer: 4x⁴+3x^3-11x^2-3

300

(−9v² − 8u²) + (−2uv − 2u² + v² ) + (−v² + 4uv)

Simplify: (−9v² − 8u²) + (−2uv − 2u² + v² ) + (−v² + 4uv)

-9v²+v²-v²-8u²-2u²-2uv+4uv

Combine like terms

Answer: -9v²-10u²+2uv

Subtraction

100

(a³ − 2a² ) − (3a² − 4a³ )

Simplify:(a³ − 2a² ) − (3a² − 4a³ ) 

a³+4a³-2a²-3a²

combine like terms:   a³ - 2a²

                                     - 3a³ - 3a²

Answer: 5a³-5a²

200

(3 − 6n⁵ − 8n⁴ ) − (−6n⁴ − 3n − 8n⁵)

Simplify:(3 − 6n⁵ − 8n⁴ ) − (−6n⁴ − 3n − 8n⁵)

-6n⁵+8n⁵-8n⁴+6n⁴+3n-3

Combine like terms

Answer:2n⁵-2n⁴+3n-3

300

(4x² + 7x³ y ² ) − (−6x ² − 7x³ y ² − 4x) − (10x + 9x²)

Simplify: (4x² + 7x³ y ² ) − (−6x ² − 7x³ y ² − 4x) − (10x + 9x²)

7x³y²+7x³y²+4x²+6x²-9x²+4x-10x

Combine like terms

Answer: 14x³y²+x²-6x

Multiplication

100

(4a + b)6

Simplify:(4a + b)6

Answer: 24a+6b

200

(9x + 6)(−4x + 3) 

Simplify:(9x + 6)(−4x + 3) 

-36x²+27x-24x+18

Combine like terms

Answer: -36x²+3x+18

300

(6a² - 8a + 4)(2a + 3)

Simplify: (6a² - 8a + 4)(2a + 3) 

12a³+18a²-16a²-24a+8a+12

Answer: 12a³+2a²-16a+12

Division

100

(−3x³b² ) divided by (4ab² )

Simplify: (−3x³b² )/(4ab² )

Reduce the fraction with b²

-3x³/4a

Use -a/b=a/-b=-a/b, to rewrite the fraction

Answer: -3x³  /  4a

               

200

(3x ² y ²) divided by (−4 x y) 

Simplify: (3x ² y ²)/(−4xy)

Reduce the fraction

Answer: 3xy  /  -4

300

(3a² b³ + 3ab) divided by (9ab)

Simplify:(3a² b³ + 3ab)/(9ab)

Factor the expression

3ab (ab²+1)/9ab

Reduce

Answer: ab²+1  /  3

Word Problems

100

Your school is ordering stationary. If c represents the cost of one personal chart and p is the cost of one pen. Write an expression for the total cost of 20 charts and 30 pens.

Answer: 20c+30p

200

The sides of a triangle are represented by the expressions 4x² +8, 5x² – 3x, and 4x + 6. Write the simplest expression.

4x²+8, 5x²-3x, and 4x+6
Combine like terms: 4x²+5x²-3x+4x+8+6
Answer: 9x²+x+14

300

In a bike racing, Jay gives May a 54 meter head start. After t seconds, May is at a distance 6t + 54 from the starting line and Jay is a distance of 7t from the starting line. How far ahead of Jay is May after t seconds?

(6t+54)-(7t)

combine like terms: 6t-7t+54
Answer: -t+54