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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.

4x2βˆ’10xy+16x2y2

Solution

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

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2.

βˆ’12a2b3c4+18ab3c5βˆ’60ab2c4

Solution

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

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3.

45x7y11+75x6y12+15x6y9

Solution

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

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9.

x2y+4xβˆ’3xy2βˆ’12y

Solution

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

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10.

12x2+8xβˆ’21xβˆ’14

Solution

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

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11.

4a2bβˆ’8ab2+aβˆ’2b

Solution

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

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25.

3x3βˆ’81y15

Solution

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

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26.

4x2βˆ’16y12

Solution

\(4x^2-16y^{12}=4(x-2y^6)(x+2y^6)\)

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28.

20x2βˆ’3xyβˆ’2y2

Solution

\(20x^2-3xy-2y^2=(4x+y)(5x-2y)\)

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30.

xy4+6x2y3βˆ’40x3y2

Solution

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