Exercise 23 Page 265

We can square the expression by writing it as the product of two binomials and then using the Distributive Property.

(4-sqrt(5))^2

PowToProdTwoFac

a^2=a* a

(4-sqrt(5))(4-sqrt(5))

Distr

Distribute (4-sqrt(5))

4(4-sqrt(5))-sqrt(5)(4-sqrt(5))

▼

Distribute 4 & -sqrt(5)

Distr

Distribute 4

4(4)-4sqrt(5)-sqrt(5)(4-sqrt(5))

Distr

Distribute -sqrt(5)

4(4)-4sqrt(5)-sqrt(5)(4) -sqrt(5)(- sqrt(5))

Multiply

Multiply

16-4sqrt(5)-4sqrt(5)-sqrt(5)(- sqrt(5))

MultNegNegOnePar

- a(- b)=a* b

16-4sqrt(5)-4sqrt(5)+sqrt(5)* sqrt(5)

MultSqrt

sqrt(a)* sqrt(a)= a

16-4sqrt(5)-4sqrt(5)+5

CommutativePropAdd

Commutative Property of Addition

16+5-4sqrt(5)-4sqrt(5)

AddSubTerms

Add and subtract terms

21-8sqrt(5)