Multiplying parenthetical terms is an application of the Distributive Property. Each term of the first expression multiplies each term of the second expression. (a+b)(c+d+e)⇓a(c+d+e)+b(c+d+e) If needed, the Distributive Property can be used again to find the required product. (a+b)(c+d+e)⇓a(c+d+e)+b(c+d+e)⇓ac+ad+ae+bc+bd+be A particular example is shown below.
(x3+x2+5)(x4+2x+1)=(x3+x2+5)(x4+2x+1)= x3(x4+2x+1)+x2(x4+2x+1)+ 5 (x4+2x+1) x7+2x4+x3+ x6+2x3+x2+5x4+10x+5
Usually, it is possible simplify the result by combining like terms.
(x3+x2+5)(x4+2x+1)=(x3+x2+5)(x4+2x+1)= x7+2x4+x3+ x6+2x3+x2+5x4+10x+5 x7+7x4+3x3+ x6+ x2+10x+ 5