16x4 – y4
Factorise it plz
Answers
a^2-b^2 = (a+b)(a-b)
Step-by-step explanation:
16x^4-y^4
= (4x^2)^2-(y^2)^2
= (4x^2+y^2)(4x^2-y^2)
= (4x^2+y^2)(2x+y)(2x-y)
Step-by-step explanation:
Step by Step Solution:-
(1): "y4" was replaced by "y^4". 1 more similar replacement(s).
STEP1:Equation at the end of step 1
24x4 - y4
STEP2:
Trying to factor as a Difference of Squares:
2.1 Factoring: 16x4-y4
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 : x4 is the square of x2
Check : y4 is the square of y2
Factorization is : (4x2 + y2) • (4x2 - y2)
Trying to factor as a Difference of Squares:
2.2 Factoring: 4x2 - y2
Check : 4 is the square of 2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (2x + y) • (2x - y)
Final result :
(4x2 + y2) • (2x + y) • (2x - y)