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Section 4.8 Additional Practice Factoring

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Exercises Exercises

Completely factor each expression.

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1.

4x^2-10xy+16x^2y^2

Solution

\(4x^2-10xy+16x^2y^2=2x(2x-5y+8xy^2)\)

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2.

-12a^2b^3c^4+18ab^3c^5-60ab^2c^4

Solution

\(-12a^2b^3c^4+18ab^3c^5-60ab^2c^4=-6ab^2c^4(2ab-3bc+10)\)

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3.

45x^7y^{11}+75x^6y^{12}+15x^6y^9

Solution

\(45x^7y^{11}-75x^6y^{12}+15x^6y^9=15x^6y^9(3xy^2-5y^3+1)\)

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9.

x^2y+4x-3xy^2-12y

Solution

\(x^2y+4x-3xy^2-12y=(xy+4)(x-3y)\)

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10.

12x^2+8x-21x-14

Solution

\(12x^2+8x-21x-14=(3x+2)(4x-7)\)

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11.

4a^2b-8ab^2+a-2b

Solution

\(4a^2b-8ab^2+a-2b=(a-2b)(4ab+1)\)

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25.

3x^3-81y^{15}

Solution

\(3x^3-81y^{15}=3(x-3y^5)(x^2+3xy^5+9y^{10})\)

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30.

xy^4+6x^2y^3-40x^3y^2

Solution

\(xy^4+6x^2y^3-40x^3y^2=xy^2(y-4x)(y+10x)\)