factorise the expression x⁴-y⁴
Answers
Answer:
(x2 + y2) • (x + y) • (x - y)
Step-by-step explanation:
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 : x4 is the square of x2
Check : y4 is the square of y2
Factorization is : (x2 + y2) • (x2 - y2)
Trying to factor as a Difference of Squares:
1.2 Factoring: x2 - y2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (x + y) • (x - y)
Final result :
(x2 + y2) • (x + y) • (x - y)
Step-by-step explanation:
given=x⁴-y⁴
(x²)²-(y²)²
algebraic identity =a²-b²=(a+b) (a-b)
(ײ+y²) (x²-y²)
=(x+y ) (x-y)
i hope that it will help u