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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Multiplying Polynomials

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Exercise 33 Page 25

Start by writing expressions for the areas of the circle and rectangle.

4π x^2+12π x+9π-3x^2-5x-2

Practice makes perfect

We want to write an expression that represents the area of shaded region. We need to subtract the area of the rectangle from the area of the circle.

Let's first write expressions for the areas of the circle and rectangle. Area of Circle [0.5em] A_c= π r^2 [0.5em] A_c= π ( 2x+3)^2 [1.0em] Area of Rectangle [0.5em] A_r= l * w [0.5em] A_r=( 3x+2)( x+1) [0.5em] The shaded area is equal to A_c-A_r. A_c-A_r ⇕ π (2x+3)^2-(3x+2)(x+1) Recall that the exponent 2 indicates that (2x+3) is used as a factor twice. Let's use it and then the FOIL method to simplify it.

π (2x+3)^2-(3x+2)(x+1)

PowToProdTwoFac

a^2=a* a

π (2x+3)(2x+3)-(3x+2)(x+1)

▼

Simplify

Multiply parentheses

π [(2x)(2x)+(2x)(3)+(3)(2x)+(3)(3)]-[(3x)(x)+(3x)(1)+(2)(x)+(2)(1)]

Multiply

π [4x^2+6x+6x+9-[3x^2+3x+2x+2]

Add terms

π [4x^2+12x+9]-[3x^2+5x+2]

Distribute π

4π x^2+12π x+9π-[3x^2+5x+2]

Distribute -1

4π x^2+12π x+9π-3x^2-5x-2

The area of shaded region is 4π x^2+12π x+9π-3x^2-5x-2.

Subchapter links

Exercises p.25-27