how to factorize a^4b^4-16c^4
pl solve
Answers
a4b4-16c4
Final result :
(a2b2 + 4c2) • (ab + 2c) • (ab - 2c)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((a4) • (b4)) - 24c4
Step 2 :
Trying to factor as a Difference of Squares :
2.1 Factoring: a4b4-16c4
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 : 16 is the square of 4
Check : a4 is the square of a2
Check : b4 is the square of b2
Check : c4 is the square of c2
Factorization is : (a2b2 + 4c2) • (a2b2 - 4c2)
Trying to factor as a Difference of Squares :
2.2 Factoring: a2b2 - 4c2
Check : 4 is the square of 2
Check : a2 is the square of a1
Check : b2 is the square of b1
Check : c2 is the square of c1
Factorization is : (ab + 2c) • (ab - 2c)
Final result :
(a2b2 + 4c2) • (ab + 2c) • (ab - 2c)