Applying Polynomial Identities

  • 10th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
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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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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 10 | Updated: Jan 20, 2026
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1) Expand (x − 6)²

Explanation

(x − 6)² = x² − 2·x·6 + 6² = x² − 12x + 36.

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About This Quiz
Applying Polynomial Identities - Quiz

Polynomial identities are powerful shortcuts in algebra. In this quiz, you’ll put them into action—expanding, simplifying, and solving expressions more efficiently. Take this quiz to boost your problem-solving speed and confidence.

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2) Expand (5x + 4)²

Explanation

(5x + 4)² = 25x² + 2·5x·4 + 16 = 25x² + 40x + 16.

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3) Simplify (2x − 3)(2x + 3)

Explanation

This is a difference of squares: (a − b)(a + b) = a² − b² = (2x)² − 3² = 4x² − 9.

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4) Expand (x + 2)(x² − 2x + 4)

Explanation

This is the sum of cubes pattern: (x + 2)(x² − 2x + 4) = x³ + 2³.

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5) Simplify (3x − 5)(3x + 5)

Explanation

Again, difference of squares: (3x)² − 5² = 9x² − 25.

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6) If a = 50 and b = 1, use (a + b)² to find (a + b)² quickly.

Explanation

(50 + 1)² = 51² = 2601 using the identity (a + b)².

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7) Which identity would you use to expand (x + y)²?

Explanation

The standard expansion for (x + y)² uses the formula a² + 2ab + b².

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8) Expand (x − 8)(x + 8)

Explanation

Difference of squares: x² − 8² = x² − 64.

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9) Which identity can simplify 100² − 99² mentally?

Explanation

a² − b² = (a − b)(a + b) = (100 − 99)(100 + 99) = 1×199 = 199.

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10) Which expression is equivalent to (2x − 3)²?

Explanation

(2x − 3)² = 4x² − 2·2x·3 + 9 = 4x² − 12x + 9.

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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 (x − 6)²
Expand (5x + 4)²
Simplify (2x − 3)(2x + 3)
Expand (x + 2)(x² − 2x + 4)
Simplify (3x − 5)(3x + 5)
If a = 50 and b = 1, use (a + b)² to find (a + b)² quickly.
Which identity would you use to expand (x + y)²?
Expand (x − 8)(x + 8)
Which identity can simplify 100² − 99² mentally?
Which expression is equivalent to (2x − 3)²?
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