Easy Algebra Step-by-Step

102 Easy Algebra Step-by-Step

c. ()))))(((()(^2

Step 1. Multiply all the terms of the second polynomial by each term of the

fi rst polynomial.

()x )()(xx + xx+

=xx⋅^22 ++⋅xx⋅ 24 x++⋅xxx⋅ − 22 ⋅x^2 − ⋅ 22 xx− ⋅ 4

=+xx^32 ++ 24 x^2 + xx−− 24 x^22 − x− 8

Step 2. Simplify.

=−x^38

Special Products

The answer to the last problem is an example of the “difference of two

cubes.” It is a special product. Here is a list of special products that you need

to know for algebra.

Special Products

Perfect Squares

()y)^22 =xxx ++ 2 xyyy^2

()y)^22 =xxx −+ 2 xyyy^2

Difference of Two Squares

()y)()( y =xyx^22 y

Perfect Cubes

()y)^33 =xxx + 3 xx^222 yyyxy+ xyyy+^3

()y)^33 =xxx 3 xx^222 yxyyy+ xyyy^3

Sum of Two Cubes

()y)()(^22 yy)=xy^33 +y

Difference of Two Cubes

()y)()(^22 yy)=xy^33 y

P

Memorizing special products is a

winning strategy in algebra.