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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Special Products

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Exercise 51 Page 32

Use the Distributive Property.

f^3+f^2g -fg^2-g^3

Practice makes perfect

To simplify the given expression we will use the Distributive Property.

(f+g)(f-g)(f+g)

Distribute (f+g)

(f+g) ( f(f+g)-g(f+g) )

▼

Distribute f & - g

Distribute f

(f+g) ( f^2+fg-g(f+g) )

Distribute - g

(f+g) ( f^2+fg-fg-g^2 )

Subtract term

(f+g) ( f^2-g^2 )

Distribute ( f+g )

f^2 ( f+g ) -g^2( f+g)

▼

Distribute f^2 & - g^2

Distribute f^2

f^3+f^2g -g^2( f+g)

Distribute - g^2

f^3+f^2g -fg^2-g^3

Alternative Solution

Using the Difference of Squares

We can also simplify the expression by using the difference of squares.

(f+g)(f-g)(f+g)

ExpandDiffSquares

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

( f^2-g^2 ) (f+g)

Distribute (f+g)

f^2(f+g)-g^2(f+g)

▼

Distribute f^2 & - g^2

Distribute f^2

f^3+f^2g-g^2(f+g)

Distribute - g^2

f^3+f^2g-fg^2-g^3

Subchapter links

Exercises p.30-33