Simplifying
Simplying is combining like terms or cancelling common factors in fractions.
Combining like terms
Terms are called "like terms" when they
have the same unknowns (for example, x) to the same power. Their coefficients (the numbers in front of each term) can be the same or different.
The result of the example expansion on the expanding page has 8 terms, but only 5 different
unknown and exponent combinations. We'll write the like terms next to
each other then combine the like terms.
48x^{2} +
24x^{3} + 12x^{4} +
6x^{5}  24x^{3} 
12x^{4}  6x^{5} 
3x^{6}
= 48x^{2} + 24x^{3} 
24x^{3} + 12x^{4} 
12x^{4} + 6x^{5} 
6x^{5}  3x^{6}
= 48x^{2} + 0x^{3} ^{} +
0x^{4} + 0x^{5} 
3x^{6}
= 48x^{2} ^{} ^{}  3x^{6} 
And so we have our expanded and simplified answer.
3x^{2}(4 + x^{2})(2 + x)(2
 x) = 48x^{2} ^{} ^{}  3x^{6}
