Question

x4 + y4 - 7x2y2
factorise it

Answer 1

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)

Answer 2

Please see the attachment