Grade 11 · Math · Algebra 2

11th grade Polynomial identities and the Binomial Theorem worksheet

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Polynomial identities and the Binomial Theorem

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Pia squares x² + 3 on a worksheet with an area model of four pieces. Type powers like x^4. What is (x² + 3)²?
In a notebook, Ren draws a square with sides x² − 5 and cuts it into four pieces. Type powers like x^4. What is its area?
Tala expands (x² + 4)² in pencil, piece by piece. Type powers like x^4. What is it in fewest terms?
On a worksheet, the Pascal row for power 5 is 1, 5, 10, 10, 5, 1. Esme builds the row for power 6. What is its third number?
In a notebook, Jun writes the Pascal row for power 6: 1, 6, 15, 20, 15, 6, 1. What is the third number of the next row?
Kira copies the Pascal row 1, 7, 21, 35, 35, 21, 7, 1 in pencil and starts the row under it. What is the fourth number of the new row?
On a puzzle card, the Pascal row for power 8 is 1, 8, 28, 56, 70, 56, 28, 8, 1. Luz wants the next row. What is its third number?
8.
On a worksheet, Milo checks four equations. Which one is true for every value of the letters?
- (x³ + 2)² = x⁶ + 2x³ + 4
- (x³ + 2)² = x⁶ + 4x³ + 4
- (x³ + 2)² = x⁶ − 4
- (x³ + 2)² = x⁶ + 4
9.
In a notebook, Noah tests which equation is an identity (true for every value). Which one is it?
- (x³ − 5)² = x⁶ − 5x³ + 25
- (x³ − 5)² = x⁶ − 10x³ + 25
- (x³ − 5)² = x⁶ + 25
- (x³ − 5)² = x⁶ + 10x³ + 25
10.
On a puzzle card, Ren must pick the identity (true for every value). Which one is it?
- (x² − 4y)² = x⁴ − 4x²y + 16y²
- (x² − 4y)² = x⁴ + 16y²
- (x² − 4y)² = x⁴ − 8x²y + 16y²
- (x² − 4y)² = x⁴ + 8x²y + 16y²

11th grade Polynomial identities and the Binomial Theorem worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Polynomial identities and the Binomial Theorem. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can expand a square or cube of a binomial and check an identity.
I can use an identity to make whole-number right triangles.
I can use Pascal's triangle to expand (x + a)ⁿ or find one coefficient.

Standard: A-APR.C.4, A-APR.C.5 (+), N-CN.C.8 (+)

Words to know

identity: An equation true for every value of its letters.

Pascal's triangle: Rows of numbers; each is the sum of the two above it.

coefficient: The number in front of a term.

Binomial Theorem: Pascal's numbers give every term of (x + y)ⁿ.

Common mistakes

Your child squared or cubed only the two ends and left out the middle parts, as in (a + b)² = a² + b². Try: draw the square and name all four pieces.

Your child counted the middle piece of a square once instead of twice. Try: draw the square and count the two matching strips.

Your child expanded a power of a difference with every sign plus. Try: write the second term with its minus sign and raise it to each power.

Questions parents ask

What is the most common mistake with polynomial identities and the binomial theorem?

Your child squared or cubed only the two ends and left out the middle parts, as in (a + b)² = a² + b². Try: draw the square and name all four pieces.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

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