body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Multiplying Polynomials

Continue to next subchapter

Exercise 38 Page 26

Apply the Distributive Property.

9c^2+24cd+16d^2

Practice makes perfect

We can find the product of this expression using polynomial identities. In this case, we have the square of a binomial. We will first rewrite the square as the product and then apply the Distributive Property.

(3c+4d)^2

PowToProdTwoFac

a^2=a* a

(3c+4d)(3c+4d)

Distribute (3c+4d)

3c(3c+4d)+4d(3c+4d)

Distribute 3c

9c^2+12cd+4d(3c+4d)

Distribute 4d

9c^2+12cd+12cd+16d^2

Add terms

9c^2+24cd+16d^2

Alternative Solution

Expanding Positive Perfect Square

We can also simplify the expression by expanding the positive perfect square trinomial.

(3c+4d)^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

(3c)^2+2(3c)(4d)+(4d)^2

(a b)^m=a^m b^m

3^2c^2+2(3c)(4d)+4^2d^2

Calculate power

9c^2+2(3c)(4d)+16d^2

Multiply

9c^2+24cd+16d^2

Subchapter links

Exercises p.25-27