Question

Divide by factorisation a^4-b^4÷a+b​

Answer 1

Answer:

a2+b2 . (a+b)

Step-by-step explanation:

Trying to factor as a Difference of Squares :

1.1 Factoring: a4 - b4

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 : a4 is the square of a2

Check : b4 is the square of b2

Factorization is : (a2 + b2) • (a2 - b2)

Trying to factor as a Difference of Squares :

1.2 Factoring: a2 - b2

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Canceling Out :

1.3 Cancel out (a - b) which appears on both sides of the fraction line.

Final result :

(a2 + b2) • (a + b)