## Week 10 – Difference of squares

This week in math we looked over the difference of squares, a a concept we discovered in week 9 where you use the method as a way of skipping the distributive method while evaluating your expression.

The method works as follows:

(a+b) (a-b)

= $a^2$ + ab – ba – $b^2$

= $a^2$$b^2$

This can be used to work backwards as well, when factoring expressions.

Example:

75$x^2$$y^2$ -3

First we remove the common factor,

3 (25$x^2$$y^2$ -1)

Then we factor.

3 (5xy – 1) (5xy + 1)

## Week 9- Recognizing Polynomial Patterns

This week in math 10 we learned how to recognize patters within polynomial expressions and evaluate them. These patterns can be remembered and then applied to skip over distributive property steps and evaluate the expressions quicker.

The patterns:

(a+b) (a-b)

= $a^2$ + ab – ba – $b^2$

= $a^2$$b^2$

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

= $a^2$ + ab + ba + $b^2$

= $a^2$ + 2ab + $b^2$

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

= $a^2$ -ab -ba + $b^2$

= $a^2$ -2ab + $b^2$