Exercise 82 Page 84

To solve the given equation by factoring, we will start by identifying the values of a, b, and c. 4y^2=64 ⇔ 4y^2+ 0y+( - 64)=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

4y^2-64=0

WritePow

Write as a power

2^2y^2-8^2=0

PowProdII

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

(2y)^2-8^2=0

FacDiffSquares

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

(2y+8)(2y-8)=0

Now we are ready to use the Zero Product Property.

(2y+8)(2y-8)=0

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Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc2y+8=0 & (I) 2y-8=0 & (II)

SubEqn

(I): LHS-8=RHS-8

lc2y=- 8 & (I) 2y-8=0 & (II)

DivEqn

(I): .LHS /2.=.RHS /2.

lcy=- 4 & (I) 2y-8=0 & (II)

AddEqn

(II): LHS+8=RHS+8

lcy=- 4 & (I) 2y=8 & (II)

DivEqn

(II): .LHS /2.=.RHS /2.

lcy=- 4 & (I) y=4 & (II)

We found that the solutions to the given equation are y=- 4 and y=4. To check our answer, we will graph the related function f(y)=4y^2-64 using a calculator. Note that in the calculator we will use the variable x instead of y.

We can see that the x-intercepts are - 4 and 4. Therefore, our solutions are correct.