Question

(a^2-b^2)c+(b^2-c^2)a​

Answer 1

Answer:

a2c + ab2 - ac2 - b2c

Step-by-step explanation:

STEP

1

:

Trying to factor as a Difference of Squares

1.1 Factoring: b2-c2

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 : b2 is the square of b1

Check : c2 is the square of c1

Factorization is : (b + c) • (b - c)

Equation at the end of step

1

:

(((a2)-(b2))•c)+a•(b+c)•(b-c)

STEP

2

:

Trying to factor as a Difference of Squares

2.1 Factoring: a2-b2

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Equation at the end of step

2

:

c•(a+b)•(a-b)+a•(b+c)•(b-c)

STEP

3

:

Final result :

a2c + ab2 - ac2 - b2c