Factoring the Sum or Difference of Two Cubes The Sum of Cubes ...
Factoring the Sum or Difference of Two Cubes The Sum of Cubes ...
Factoring the Sum or Difference of Two Cubes The Sum of Cubes ...
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Answers<br />
Fact<strong>or</strong>:<br />
8a<br />
+ b<br />
3 3<br />
We begin by rewriting each term as a cube and use <strong>the</strong> sum <strong>of</strong> cubes f<strong>or</strong>mula as<br />
a guide.<br />
( )( )<br />
x + y = x + y x − xy + y<br />
3 3 2 2<br />
( )( )<br />
8 a + b = (2 a) + ( b) = 2 a+ b (2 a) − (2 a)( b) + ( b)<br />
3 3 3 3 2 2<br />
So simplifying <strong>the</strong> right hand side we get:<br />
( )( )<br />
3 3 2 2<br />
8a + b = 2a+ b 4a − 2ab+ b Answer<br />
Fact<strong>or</strong>:<br />
8a<br />
− b<br />
3 3<br />
We begin by rewriting each term as a cube and use <strong>the</strong> difference <strong>of</strong> cubes<br />
f<strong>or</strong>mula as a guide.<br />
( )( )<br />
x − y = x − y x + xy + y<br />
3 3 2 2<br />
( )( )<br />
8 a − b = (2 a) − ( b) = 2 a− b (2 a) + (2 a)( b) + ( b)<br />
3 3 3 3 2 2<br />
So simplifying <strong>the</strong> right hand side we get:<br />
( )( )<br />
3 3 2 2<br />
8a − b = 2a− b 4a + 2ab+ b Answer<br />
Fact<strong>or</strong>:<br />
8a<br />
+ 27b<br />
3 3<br />
We begin by rewriting each term as a cube and use <strong>the</strong> sum <strong>of</strong> cubes f<strong>or</strong>mula as<br />
a guide.<br />
( )( )<br />
x + y = x + y x − xy + y<br />
3 3 2 2<br />
( )( )<br />
8a + 27 b = (2 a) + (3 b) = 2a+ 3 b (2 a) − (2 a)(3 b) + (3 b)<br />
3 3 3 3 2 2<br />
So simplifying <strong>the</strong> right hand side we get:<br />
( )( )<br />
3 3 2 2<br />
8a + 27b = 2a+ 3b 4a − 6ab+ 9b<br />
Answer
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