Question

Factorize (a^2-b^2)(c^2-d^2) ​-4abcd​

Answer 1

Step-by-step explanation:

a2-b2)(c2-d2)-4abcd

Final result :

a2c2 - a2d2 - 4abcd - b2c2 + b2d2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "d2" was replaced by "d^2". 3 more similar replacement(s).

Step by step solution :

Step 1 :

Trying to factor as a Difference of Squares :

1.1 Factoring: a2-b2

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 : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Trying to factor as a Difference of Squares :

1.2 Factoring: c2 - d2

Check : c2 is the square of c1

Check : d2 is the square of d1

Factorization is : (c + d) • (c - d)

Equation at the end of step 1 :

(a+b)•(a-b)•(c+d)•(c-d)-4abcd

Step 2 :

Final result :

a2c2 - a2d2 - 4abcd - b2c2 + b2d2

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