Simplifying expressions

Change the sign

100

Simplify the expression

-(2x+1)

-2x-1

200

Which of the following is the simplified form 

of -(-5x²+3-4x)?

a. 5x²+7x

b. -5x²+3-4x

c. 5x²-3+4x

c

300

Is the following an expression? Why or why not?

2x+9x⁵=4

No, expressions do not involve equal signs.

400

Can the following expression be simplified? Why or why not?

4x+9-3x²+25y-6x⁶

No, none of the terms are like terms. They do not have the same variables or exponents.

500

Simplify the expression.

-(2x-8+5y-24x²)

-2x+8-5y+24x²

Identify Like terms

100

Which of the following is a like term for 3x²?

Select all that apply.

a. 5x²

b. 3y²

c. 3x^-2

d. 3²

e. 9x²

a, e

200

Which of the following can be combined with 2x^-4?

Select all that apply.

a. 2x

b.x⁴

c. -x

d. 4x⁴

e. none of the above

e

300

Two terms are given: 2x² and 5y.Can these two terms be combined? If not, what should be changed in the term 5y to allow it to combine with 2x²?

You can change the 5y to a 5x²

400

Simplify the expression.

4x+3y-2+7x²+2y+8

4x+5y+6+7x²

500

Simplify the following expression.

2x²+1-4x²+9-2x

-2x²+8+2x

Combine like terms

100

Combine like terms in the expression.

2xy+5x-3+4xy

6xy+5x-3

200

Simplify the expression.

4x⁸y²+3x⁸-4+9x⁸y²

13x⁸y²+3x⁸-4

300

Look at the two expressions. Is the second expression a simplified form of the first? Why?

-(4x)

4x

No, the simplified form would be -4x because the negative sign should be distributed to each term in parentheses.

400

Can the following terms be combined? Explain why or why not.

3x²y⁵ and 7xy

No, the exponents are not the same on each term.

500

Look at the following term.

4x²y⁵z⁷

Pete figured he could combine it with the following term: 

4xyz

Is he correct? Can he combine the two terms? Why or why not?

No, they need to have the same exponents. Coefficients and variables alone are not enough.

Simplify

100

Look at the two expressions. Is the second expression a simplified form of the first?WHy?

4x-2+8x-12x²

12x-10x²

No, the simplified form would be 12x-2-12x².

200

Which of the following can be combined with 2x^-4?

Select all that apply.

a. 2x

b. x⁴

c. -x

d. 4x⁴

e. none of the above

e

300

Simplify each of the following expressions.

1. -(2x+9-4y)

2. -(x+9-4x²)

3. 4x+(-4x+9)

-2x-9+4y

-x-9+4x²

9

400

Simplify the following expression.

(6x²y³+5x-2x²y³)-(-4x+8xy⁵)

4x²y³+9x+8xy⁵

500

A student simplified an expression. His work is shown below.

1. (4x⁵-2y+8)-(6x⁵+3-2y)

2. 4x⁵-2y+8-6x⁵-3+2y

3. 2x⁵+4y+5

Did he make a mistake? If he did, what went wrong and how can he fix it?

2x⁵ should be negative and there should be no more y. -2y+2y=0. The simplified expression should be -2x⁵+5

Multiply & Divide

100

(-2)(8x)(-1x²)
-----------------

         x³

16

200

4x times 4xy²

16x²y²

300

ab²c*abc*a²bc³

^{-----------------------}

abc⁵

a³b³

400

Daily double

Simplify.(5x²)(2x)(+6)(-x³) divided by (2x²)²

-15x²

500

(2x)(-3x+5-2x²) divided by 2x

(must write terms from largest x power to lowest x power)

-3+5-2x²