Exercises: Rewrite Expressions Using Structure

For each problem, first identify the pattern or structure, then apply the appropriate strategy. Always verify your factored form by expanding or checking at a test value.

Grade 9·21 problems·~45 min·Common Core Math - HS Algebra·standard·hsa-sse-a-2

Work through problems with immediate feedback

Recall / Warm-Up

Expand $(x + 5)(x - 5)$ .

$x^2 + 25$

$x^2 - 25$

$x^2 + 10x - 25$

$x^2 - 10x - 25$

Which of the following is a perfect square?

$9x^2$

$4x^3$

$12x^4$

$6x^2$

Expand $(x - 3)^2$ .

$x^2 - 9$

$x^2 + 6x + 9$

$x^2 - 6x + 9$

$x^2 - 3x + 9$

Fluency Practice

Factor $x^2 - 49$ completely.

$(x - 7)^2$

$(x + 7)(x + 7)$

$(x + 7)(x - 7)$

$(x - 7)(x - 7)$

Factor $x^2 - 8x + 16$ completely.

$(x - 4)^2$

$(x - 4)(x + 4)$

$(x + 4)^2$

$(x - 2)^2$

Factor $x^3 - 27$ completely.

$(x - 3)^3$

$(x - 3)(x^2 + 3x + 9)$

$(x - 3)(x^2 - 3x + 9)$

$(x + 3)(x^2 - 3x + 9)$

Which expression is equivalent to $x^4 - 16$ after one application of the difference-of-squares pattern?

$(x^2 + 4)(x^2 - 4)$

$(x^2 - 4)^2$

$(x + 4)(x - 4)(x + 4)(x - 4)$

$(x^2 + 16)(x^2 - 16)$

Factor $4x^2 - 12x + 9$ completely.

$(2x - 3)^2$

$(4x - 9)(x - 1)$

$(2x - 3)(2x + 3)$

$(2x + 3)^2$

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