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ab • (a + b) • (a - b)
Explanation:
a3b-b3a
Step by step solution :
Step 1 :
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
a3b - ab3 = ab • (a2 - b2)
Trying to factor as a Difference of Squares :
2.2 Factoring: a2 - b2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (a + b) • (a - b)
Final result :
ab • (a + b) • (a - b)