Identifying and Applying Basic Polynomial Identities

  • 9th Grade
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| Attempts: 23 | Questions: 10 | Updated: Jan 20, 2026
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1) Expand (2x − 7)(2x + 7)

Explanation

Difference of squares: (2x)² − 7² = 4x² − 49.

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About This Quiz
Identifying and Applying Basic Polynomial Identities - Quiz

Algebra is full of patterns waiting to be unlocked! In this quiz, you’ll practice spotting and using basic polynomial identities like squares and cross products. Try this quiz to strengthen your foundation in algebraic manipulation.

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2) Which expression matches (2x + 3)²?

Explanation

Expand using (a+b)² → (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9.

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3) Which identity is used to expand (x − 4)²?

Explanation

The square of a difference identity.

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4) Expand (x + 5)²

Explanation

Using (a+b)² = a² + 2ab + b², here a = x and b = 5.

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5) Simplify (4x − 5)(4x + 5)

Explanation

(a+b)(a−b) = a² − b² → (4x)² − 5².

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6) Simplify (x + 7)(x − 7)

Explanation

(a+b)(a−b) = a² − b².

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7) Simplify (y + 6)²

Explanation

(a+b)² with a = y and b = 6 → y² + 12y + 36.

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8) Which expression equals (a + b)²?

Explanation

Standard expansion of the square of a sum.

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9) Using (a+b)², find 99² quickly by writing it as (100 − 1)².

Explanation

(100−1)² = 100² − 2(100)(1) + 1² = 10000 − 200 + 1 = 9801.

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10) Expand (3x − 2)²

Explanation

(a−b)² = a² − 2ab + b² → 9x² − 12x + 4.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Expand (2x − 7)(2x + 7)
Which expression matches (2x + 3)²?
Which identity is used to expand (x − 4)²?
Expand (x + 5)²
Simplify (4x − 5)(4x + 5)
Simplify (x + 7)(x − 7)
Simplify (y + 6)²
Which expression equals (a + b)²?
Using (a+b)², find 99² quickly by writing it as (100 − 1)².
Expand (3x − 2)²
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