Exercise 44 Page 31

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

(r+2)(r-5)(r-2)(r+5)

Distr

Distribute (r+5)

(r+2)(r-5) ( r(r+5)-2(r+5) )

▼

Distribute r & - 2

Distr

Distribute r

(r+2)(r-5) ( r^2+5r-2(r+5) )

Distr

Distribute - 2

(r+2)(r-5) ( r^2+5r-2r-10 )

SubTerm

Subtract term

(r+2)(r-5) ( r^2+3r-10 )

Distr

Distribute ( r^2+3r-10 )

(r+2) ( r(r^2+3r-10)-5(r^2+3r-10) )

▼

Distribute r & - 5

Distr

Distribute r

(r+2) ( r^3+3r^2-10r-5(r^2+3r-10) )

Distr

Distribute - 5

(r+2)( r^3+3r^2-10r-5r^2-15r+50 )

SubTerms

Subtract terms

(r+2)( r^3-2r^2-25r+50 )

Distr

Distribute (r^3-2r^2-25r+50)

r( r^3-2r^2-25r+50 )+2( r^3-2r^2-25r+50 )

▼

Distribute r & 2

Distr

Distribute r

r^4-2r^3-25r^2+50r+2( r^3-2r^2-25r+50 )

Distr

Distribute 2

r^4-2r^3-25r^2+50r+2r^3-4r^2-50r+100

AddSubTerms

Add and subtract terms

r^4-29r^2+100

Alternative Solution

Using the Difference of Squares

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

(r+2)(r-5)(r-2)(r+5)

CommutativePropMult

Commutative Property of Multiplication

(r+2)(r-2)(r+5)(r-5)

ExpandDiffSquares

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

(r^2-2^2)(r^2-5^2)

CalcPow

Calculate power

(r^2-4)(r^2-25)

Distr

Distribute (r^2-4)

r^2(r^2-4)-25(r^2-4)

▼

Distribute r^2 & - 25

Distr

Distribute r^2

r^4-4r^2-25(r^2-4)

Distr

Distribute - 25

r^4-4r^2-25r^2+100

SubTerm

Subtract term

r^4-29r^2+100

Hints

Check the answer

Practice exercises

Asses your skill

Alternative Solution