Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 495: 35

$5x(4x-1)$ Drawing a diagram can help to know what needs to be subtracted from what. The wooden part is the difference between the whole frame and the opening.

Work Step by Step

The opening has the area $A_{1}=3x\cdot 5x=15x^{2}$ The whole frame has the area $A_{2}=5x\cdot(7x+1)\qquad...$apply the Distributive Property. $A_{2}=35x^{2}+5x$ The area of the wooden part of the frame is $A_{2}-A_{1}=35x^{2}+5x-15x^{2}=20x^{2}-5x$. $20x^{2}-5x\qquad...$find the GCF. $20x^{2}=2\cdot 2\cdot(5)\cdot(x)\cdot x$ $-5x=-1\cdot(5)\cdot(x)$ GCF=$(5)\cdot(x)$, or $5x$. $20x^{2}-5x\qquad...$factor out the GCF $=5x(4x)-5x(1)\qquad...$apply the Distributive Property. $=5x(4x-1)$ The factored form of the area of the wooden part of the frame is $5x(4x-1)$. Drawing a diagram can help to know what needs to be subtracted from what. The wooden part is the difference of the whole frame and the opening.

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