Polynomials & Functions
Distributive Property with Polynomials
The distributive property lets you multiply a term by everything inside parentheses: a(b + c) = ab + ac. With polynomials, multiply each term carefully.
Watch & Learn
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Expand: 3x(2x² − 4x + 5)
Step-by-Step Solution
Multiply 3x by each term inside.
3x × 2x² = 6x³
3x × (−4x) = −12x²
3x × 5 = 15x
Answer
6x³ − 12x² + 15x
Problem
Expand: (x + 3)(x + 5)
Step-by-Step Solution
Use FOIL: First, Outer, Inner, Last.
First: x × x = x²
Outer: x × 5 = 5x
Inner: 3 × x = 3x
Last: 3 × 5 = 15
Combine: x² + 5x + 3x + 15 = x² + 8x + 15
Answer
x² + 8x + 15
Problem
Expand: −2(3x² − x + 4)
Step-by-Step Solution
−2 × 3x² = −6x²
−2 × (−x) = 2x
−2 × 4 = −8
Answer
−6x² + 2x − 8
Problem
Expand: (x − 3)(x + 7)
Step-by-Step Solution
Use FOIL: First, Outer, Inner, Last.
First: x × x = x²
Outer: x × 7 = 7x
Inner: −3 × x = −3x
Last: −3 × 7 = −21
Combine: x² + 7x − 3x − 21 = x² + 4x − 21
Answer
x² + 4x − 21
Problem
Expand: 5x²(2x − 3)
Step-by-Step Solution
5x² × 2x = 10x³
5x² × (−3) = −15x²
Answer
10x³ − 15x²
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Expand: 4(x + 7)
Expand: 2x(3x − 5)
Expand: (x + 2)(x + 6)
Expand: −3x(x² + 2x − 1)
Expand: (x − 4)(x + 4)
Expand: 5(2x − 3)
Expand: (x + 1)(x + 9)
Expand: −2x(4x + 7)
Expand: (x − 5)(x − 2)
Expand: 3x²(x − 4)
Expand: (x + 3)²
Expand: (2x + 1)(x − 3)
Finished all 12? Give yourself a pat on the back — then check your work!
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