Multiply That Monomial!
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!
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.
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
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
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.
3x(4x+2)
Multiply 3x⋅4x=12x2
Multiply 3x⋅2=6x
✅ Answer: 12x2+6x
(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.
4(x+3)
Multiply: 4⋅x=4x, 4⋅3=12
✅ Answer: 4x+12
Tip:Give the 4 to everything inside the parentheses.
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.
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.
(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!
2(x+1)+3x
First: 2x+2, then add the 3x
✅ Combine: 5x+2
Tip:After distributing, look for like terms.
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.
−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!
(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.
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.
−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!
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!
(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.
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.