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The learner will factor polynomials that are the difference of two perfect squares.

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $a^{2} - b^{2}$ completely.

$(a - b)(a - b)$
$(a - b)(a + b)$
$(a + b)(a + b)$
$2(a - b)$
cannot be factored
$(a - b)^{2}$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $x^{2}- 49$ completely.

$(x - 7)^{2}$
cannot be factored
$7x(x - 7)$
$(x + 7)(x - 7)$
$(x + 7)^{2}$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $25m^{2} -1$ completely.

cannot be factored
$5m(5m - 1)$
$(5m + 1)(5m + 1)$
$(5m - 1)(5m + 1)$
$(5m - 1)(5m - 1)$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $81x^{2} - 49y^{2}$ completely.

$(9x + 7y)(9x - 7y)$
$63xy(x - y)$
cannot be factored
$(9x-7y)^{2}$
$xy(81x - 49y)$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $100b^{2} - 16c^{2}$ completely.

$(50b - 8c)(50b + 8c)$
cannot be factored
$4(5b + 2c)(5b - 2c)$
$(10b + 4c)(10b - 4c)$
$(10b - 4c)(10b - 4c)$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $4x^{2} + 1$ completely.

$(2x + 1)^{2}$
cannot be factored
$(2x + 1)(2x - 1)$
$(4x + 1)(4x - 1)$
$(4x + 1)^{2}$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $x^{2} - 16$ completely.

$4x(x - 4)$
$(x + 4)(x - 4)$
cannot be factored
$(x + 4)(x + 4)$
$(x - 4)(x - 4)$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $25x^{2} - 64y^{4}$ completely.

cannot be factored
$(5x + 8y)(5x - 8y)$
$(5x - 8y)(5x - 8y)$
$(5x + 8y^{2})(5x - 8y^{2})$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $x^{2} - 4a^{2}b^{2}$ completely.

$(x - 2ab)(x + 2ab)$
$(x - ab)(x + 4ab)$
$(x - 4ab)(x + ab)$
cannot be factored
$(x - 4ab)^{2}$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $4x^{2} + 9$ completely.

$(4x + 3)(x + 3)$
$(2x + 9)(2x + 1)$
$(2x + 3)(2x - 3)$
$(2x + 3)(2x + 3)$
cannot be factored

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $4x^{2} - 9$ completely.

$(4x + 3)(x - 3)$
$(2x - 9)(2x + 1)$
$(2x + 3)(2x - 3)$
$(2x + 3)(2x + 3)$
cannot be factored

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $16x^{4} - 81y^{4}$ completely.

$(4x^{2} - 9y^{2})(4x^{2} + 9y^{2})$
$(4x^{2} - 9y^{2})(4x^{2} - 9y^{2})$
$(2x + 3y)(2x - 3y)(4x^{2} + 9y^{2})$
cannot be factored

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $-16 + 25k^{2}$ completely.

cannot be factored
$(-4 + 5k)(-4 - 5k)$
$(-4 + 25k)(4 + k)$
$(5k + 4)(5k - 4)$
$(-4 + 5k)^{2}$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $32x^{4} - 2$ completely.

$(16x^{2} - 1)(16x^{2} + 1)$
$(4x + 1)(4x - 1)(16x^{2} + 1)$
$2(4x^{2} + 1)(2x + 1)(2x - 1)$
cannot be factored
$(4x^{2} + 1)(4x^{2} - 1)$

Question 1 of 10

Factoring: Set 2 The Difference of Two Perfect Squares

Factor $100 - 49x^{2}$ completely.

$(25 - 7x)(4 + 7x)$
cannot be factored
$(25 + 7x)(4 - 7x)$
$(7x + 10)(7x - 10)$
$(10 - 7x)(10 + 7x)$

Question 1 of 10

Author

Kevin Ritzman

Published: 3/26/2014

Last Updated: 3/26/2014

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Factoring: Set 2 The Difference of Two Perfect Squares by Fox Valley Technical College is licensed under a Creative Commons Attribution 3.0 Unported License.