What are the factors of a3 + b3?
Answers
Answer:
An expression of the form a3 + b3 is called a sum of cubes. The factored form of a3 + b3 is (a + b)(a2 - ab + b2): (a + b)(a2 - ab + b2) = a3 + a2b - a2b - ab2 + ab2 + b3 = a3 - b3. For example, the factored form of 64x3 + 125 (a = 4x, b = 5) is (4x + 5)(16x2 - 20x + 25).
Given : a³ + b³
To Find : Factors
Solution:
a³ + b³
if (a - b) is a factor then remainder
= b³ + b³ = 2b³
if (a + b) is factor
(-b)³ + b³ = 0 Hence (a + b) is factor
Using long division :
a² - ab + b²
a + b ) a³ + b³ (
a³ + a²b
__________
b³ - a²b
-a²b -ab²
____________
b³ + ab²
b³ + ab²
____________
0
Hence
a³ + b³ = (a + b) (a² - ab + b²)
Factors are (a + b) and (a² - ab + b²)
Additional Info:
a³ - b³ = (a - b) (a² + ab + b²)
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