How to factorize x4-14x2y2+y4?
Answers
x4-7x2y2+12y4
Final result :
(x2 - 3y2) • (x + 2y) • (x - 2y)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y4" was replaced by "y^4". 3 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((x4)-((7•(x2))•(y2)))+(22•3y4)
Step 2 :
Equation at the end of step 2 :
((x4) - (7x2 • y2)) + (22•3y4)
Step 3 :
Trying to factor a multi variable polynomial :
3.1 Factoring x4 - 7x2y2 + 12y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (x2 - 3y2)•(x2 - 4y2)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2-3y2
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 : 3 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Trying to factor as a Difference of Squares :
3.3 Factoring: x2-4y2
Check : 4 is the square of 2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (x + 2y) • (x - 2y)
Final result :
(x2 - 3y2) • (x + 2y) • (x - 2y)
Read more on Brainly.in - https://brainly.in/question/8532396#readmore