Extra Practice

Multiply That Monomial!

100

What is a monomial?
Give a definition and example.

A monomial is just a math word for a number, a variable, or both multiplied together — with no plus or minus signs.

In simple terms:

A monomial is one piece like:

• Just a number → 5

• Just a letter → x

• A number and letter multiplied → 3x

• More than one letter or powers → 2x²y

Not monomials:

• x + 2 (because it has a plus)

• 3x - 5 (because it has a minus)

• If it has no plus or minus sign, it's a monomial!

200

y⁴⋅y⋅y²

All the letters are the same, so just add the little numbers on top:
4+1+2=7→ Answer: y⁷

^{Same base? Just add the little numbers on top.}

300

2a²⋅3a²

First, multiply the numbers: 2⋅3=6
Then add the exponents: a²⋅a³=a⁵
✅ Answer: 6a⁵

^{Future tip:Multiply numbers first, then letters.}

400

4x²y⋅2x³y²

Multiply the numbers: 4⋅2=8

Add exponents: x²⋅x³=x5, and y⋅y²=y³
✅ Answer: 8x⁵y³

^{Future tip:Line up each letter, then add their exponents.}

500

−3m⁴n²⋅5m²n³

Multiply numbers: −3⋅5=−15

Add exponents: m⁴⋅m²=m6, n²⋅n³=n⁵

^{Answer: −15m6n5}

^{Future tip:Don’t forget negatives — they matter when you multiply!}

Distribute That Monomial!

100

What does “distribute” mean in math?

Distribute means to give the number or variable outside the parentheses to everything inside by multiplying.
👉 Ex: 2(x+3)=2x+6

Future tip:Think of it like giving a high five to every term inside the parentheses.

200

3x(4x+2)

Multiply 3x⋅4x=12x²
Multiply 3x⋅2=6x
✅ Answer: 12x²+6x

300

2a²(3a+5)

Multiply: 2a²⋅3a=6a³, then 2a²⋅5=10a²
✅ Answer: 6a³+10a²

^{Future tip:Match up the a's and add their exponents.}

400

−4x(2x²−x+1)

Multiply each part:
−4x⋅2x2=−8x3
−4x⋅−x=+4x²
−4x⋅1=−4x
✅ Answer: −8x³+4x²−4x

Future tip:Watch those signs — negative times negative is positive!

500

5xy²(2x²y−3y²+4)

Multiply:
5xy²⋅2x²y=10x³y³
5xy²⋅−3y²=−15xy⁴
5xy²⋅4=20xy²
✅ Answer: 10x³y³−15xy⁴+20xy²

^{Future tip:Distribute one piece at a time and stay organized!}

FOIL That Binomial x trinomial!

100

What does FOIL stand for?

FOIL means: First, Outer, Inner, Last.
You multiply the two parts of each binomial in that order.
👉 Example: (x+2)(x+3)

Tip:It's just a way to stay organized when multiplying binomials

200

(x+2)(x+5)

First: x⋅x=x²
Outer: x⋅5=5x
Inner: 2⋅x=2x
Last: 2⋅5=10
✅ Answer: x²+7x+10

Tip:Add the two middle terms together at the end.

300

(x−1)(x+4)

First: x⋅x=x²
Outer: x⋅4=4x
Inner: −1⋅x=−x
Last: −1⋅4=−4
✅ Answer: x²+3x−4

Tip:Pay close attention to signs when you multiply!

400

(2x+3)(x−2)

First: 2x⋅x=2x²
Outer: 2x⋅−2=−4x
Inner: 3⋅x=3x
Last: 3⋅−2=−6
✅ Answer: 2x²−x−6

Tip:Combine like terms after FOIL to clean it up.

500

(x+1)(x2+2x+3)

First: x⋅x²=x³⋅, x⋅2x=2x², x⋅3=3x
Then: 1⋅x²=x², 1⋅2x=2x, 1⋅3=3
✅ Answer: x³+3x²+5x+3

Tip:Write everything out, then combine like terms.

Expanding & Simplifying Expressions

100

What does “simplify” mean in math?

It means to make an expression as short and clean as possible by doing all the math you can — like multiplying and combining like terms.
👉 Ex: 3x+2x=5

200

4(x+3)

Multiply: 4⋅x=4x, 4⋅3=12
✅ Answer: 4x+12

Tip:Give the 4 to everything inside the parentheses.

300

2(x+1)+3x

First: 2x+2, then add the 3x
✅ Combine: 5x+2

Tip:After distributing, look for like terms.

400

5x−2(3x−4)

Distribute: −2⋅3x=−6x, −2⋅−4=+8
Start with 5x, then add: 5x−6x+8=−x+8

Tip:Distribute the negative carefully — that’s where mistakes happen.

500

2(x−3)²−10

First: Expand (x−3)2=x2−6x+9

Multiply: 2x2−12x+18, the subtract 10

Final Answer:2x²-12x+8

Tip:Square it first, then distribute. Clean it up at the end.