Write the expression in factored form. 81m^4 - 25

Question: Factor: ab+ac ab+ac Solution: ab+ac=a (b+c) ab+ac=a (b+c)

The expression ab+ac ab+ac is a sum, since the last operation is addition.

The expression a (b+c) a (b+c) is a product, since the last operation is multiplication.

The process of factoring took us from the sum ab+ac ab+ac to the product a (b+c) a (b+c).

Notice that ab+ac=a (b+c) ab+ac=a (b+c) is just the distributive law, backwards!

In going from the name ab+ac ab+ac to the name a (b+c) a (b+c),

the common factor (aa) is first identified, and written down.

Next, an opening parenthesis ‘ (’ is inserted.

Then, the remaining parts of each term are written down.

Finally, the closing parenthesis ‘) ’ is inserted.

Question: Write in factored form: 3x-3t 3x-3t

Solution: 3 (x-t) 3 (x-t) Question: Write in factored form: 2xy-2yz 2xy-2yz Solution: 2y (x-z) 2y (x-z) Question: Write in factored form: 5 x2 - x2 y2 5 x2 - x2 y2 Solution: x2 (5 - y2) x2 (5 - y2)

Note: In the exercises below, exponents are typed in using the ‘^’ key.

For example, x2 (5 - y2) x2 (5 - y2) is typed in as x^2 (5 - y^2). Question: Write in factored form: x (2x+1) - 3 (2x+1) x (2x+1) - 3 (2x+1) Solution: (2x+1) (x-3) (2x+1) (x-3)

Note: The product (2x+1) (x-3) (2x+1) (x-3) can also be written as (x-3) (2x+1) (x-3) (2x+1).

There is no convention here about which name is ‘best’.

The exercise below recognizes both answers.

(9m^ (2) + 5) (9m^ (2) - 5)

that will be your answer