Algebraic Language and Expressions

+ or - of multivariate polynomials

100

(4x³y² + 3x² - 6x²y³) + (7x²y³ -y³ + 2x²)

4x³y² + 5x² +x²y³ -y³

200

(7x³y² + 3 -6x²y²) + (5x²y³ -4x²y²)

7x³y² + 3 - 10x²y² + 5x²y³

300

(4xy² + 5x²y -2y) + (-7x²y -6xy² + 3y)

-2x²y - 2xy²+y

400

(6x²y³ + x³y² - 7y³) + (- 2x³y² - 4x²y³ + 5y³)

2x²y³ -x³y² -2y³

500

(5x³y² +3x²y³ -6y²) - (-7x²y³ -2x³y² +y²)

7x³y² + 10x²y³ -7y²

Degree and Leading Coefficient

100

6y³-10+y+15y⁶

Degree: 6

LC: 15

200

-18w+w⁶-8w³-10

Degree: 6

LC: 1

300

-1+3u⁶-20u⁵-12u

Degree: 6 

LC: 3

400

-v⁹+20-5v⁷

Degree: 9

LC: -1

500

12y⁹+4y⁵-20-23y⁴

Degree: 9

LC: 12

Combining like terms

100

Simplify the following expression:

12x²-8+3x-2x²-10

10x²+3x-18

200

Simplify the following expression:

10x²-4+2x-8x²-15

2x²+2x-19

300

Simplify the following expression:

5x²-8-13x²+12+4x

-8x²+4x+4

400

Simplify the following expression:

4x²+6x-7-10x²

-6x²+6x-7

500

Simplify the following expression:

-7x²-6x-4x²+3+10x

-11x²+4x+3

+ or - of three univariate polynomials

100

(9y²+6y+7)+(6y²-9y-1)-(-y²-3y-7)

16y²+13

200

(8v+8)+(2v²+4v+3)-(2v²+5v-4)

7v+15

300

(-6v²+2v-6)-(5v²-7v-7)+(-5v²-6v-7)

-16v²+3v-6

400

(8u²+9u+8)+(5u²+6u-6)-(-5u²-9u+5)

18u²+24u-3

500

(-5u²-8u-6)-(-2u²-3u+8)+(3u²-7u-6)

-12u-20

Translating a sentence

100

Two less than the product of 7 and a number equals 8.

7x - 2 = 8

200

The sum of 7 times a number and 6 equals 4.

7y + 6 = 4

300

Four less than the product of 5 and a number equals 8.

5y-4 = 8

400

Nine times the sum of a number and 3 is 8.

9(c+3) = 8

500

Two more than the quotient of a number and 4 is equal to 7.

(b/4) + 2 = 7