Identifying and Applying Basic Polynomial Identities

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1) Expand (x + 5)²

Explanation

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

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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) Expand (3x − 2)²

Explanation

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

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3) Simplify (x + 7)(x − 7)

Explanation

(a+b)(a−b) = a² − b².

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4) 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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5) Simplify (4x − 5)(4x + 5)

Explanation

(a+b)(a−b) = a² − b² → (4x)² − 5².

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

Explanation

The square of a difference identity.

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8) Simplify (y + 6)²

Explanation

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

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9) Expand (2x − 7)(2x + 7)

Explanation

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

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10) Which expression equals (a + b)²?

Explanation

Standard expansion of the square of a sum.

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Expand (x + 5)²
Expand (3x − 2)²
Simplify (x + 7)(x − 7)
Which expression matches (2x + 3)²?
Simplify (4x − 5)(4x + 5)
Using (a+b)², find 99² quickly by writing it as (100 − 1)².
Which identity is used to expand (x − 4)²?
Simplify (y + 6)²
Expand (2x − 7)(2x + 7)
Which expression equals (a + b)²?
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