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

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

In a notebook, Zee tests the identity (x² + y²)² = (x² − y²)² + (2xy)² at x = 4, y = 1. What does each side equal?
Esme puts x = 5 and y = 2 into (x² + y²)² = (x² − y²)² + (2xy)² in pencil. What number is each side?
On a puzzle card, Jun makes a right triangle from (x² + y²)² = (x² − y²)² + (2xy)² with x = 4, y = 3. What is each side's value?
On a worksheet, Kira expands (x + 2)⁴ with Pascal's triangle. Type powers like x^4. What is it in fewest terms?
In a notebook, Luz uses the Binomial Theorem on (x − 1)⁵. Type powers like x^5. What is the expansion?
Milo expands (x + 3)³ in pencil using a Pascal row. Type powers like x^3. What is it in fewest terms?
On a puzzle card, Noah expands (x − 3)⁴. Type powers like x^4. What is it in fewest terms?
On a worksheet, Pia completes the identity (x + 3)² − (x − 3)² = ▢x. What number goes in the box?
In a notebook, Ren writes (x + 5)² − (x − 5)² = ▢x, true for every x. What number goes in the box?
On a puzzle card, (x + 6y)² − (x − 6y)² = ▢xy for every x and y. Zee needs the box. What number is it?

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

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

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.

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.

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.

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