Exercise 8 Page 49

Practice makes perfect

To add variables they have to be like terms. Consider the given expression.

4xy^3+5x^3y Notice the location of the exponent in each term. For the first term, the y factor is being raised, but in the second term the x factor is being raised. 4x y^3+5 x^3y Therefore, the terms are not like and we cannot add them. This means that our expression is already fully simplified.

Observing the given expression, we can see that there is a term outside the parentheses that can be distributed.

- (y-1) ⇔ - 1(y-1) Let's distribute -1.

- 1(y-1)

Distr

Distribute - 1

y(- 1)-1(- 1)

MultNegNegOnePar

- a(- b)=a* b

y(- 1)+1 * 1

MultPosNeg

a(- b)=- a * b

- y * 1+1 * 1

IdPropMult

Identity Property of Multiplication

- y+1

The given expression was not simplified, because there was a term that could be distributed. The fully simplified expression in this case should be - y+1.

Let's look at the given expression to see if there are any like terms that could be added.

5x^2+12xy-3yxThe first term has an x^2 and the second has an x0,y so these cannot be added together. However, xy and yx can be added together thanks to the Commutative Property of Multiplication.

12xy-3yx

CommutativePropMult

Commutative Property of Multiplication

12xy-3 xy

SubTerm

Subtract term

9xy

We can now write the fully simplified expression. 5x^2+9xy Therefore, the given expression was not simplified.