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.