(Factorize): 625a4 + 4b4
Answers
Step-by-step explanation:
STEP1:Equation at the end of step 1
(625 • (a4)) - 24b4
STEP 2 :
Equation at the end of step2:
54a4 - 24b4
STEP3:
Trying to factor as a Difference of Squares:
3.1 Factoring: 625a4-16b4
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 : 625 is the square of 25
Check : 16 is the square of 4
Check : a4 is the square of a2
Check : b4 is the square of b2
Factorization is : (25a2 + 4b2) • (25a2 - 4b2)
Trying to factor as a Difference of Squares:
3.2 Factoring: 25a2 - 4b2
Check : 25 is the square of 5
Check : 4 is the square of 2
Check : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (5a + 2b) • (5a - 2b)
Final result :
(25a2 + 4b2) • (5a + 2b) • (5a - 2b)