Question

2
5. Factorise 32x® - 8xy​

Answer 1

32x3-8xy

Final result :

8x • (4x2 - y)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3" was replaced by "x^3".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

25x3 - 8xy

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

32x3 - 8xy = 8x • (4x2 - y)

Trying to factor as a Difference of Squares :

3.2 Factoring: 4x2 - y

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 : 4 is the square of 2

Check : x2 is the square of x1

Check : y1 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares

Final result :

8x • (4x2 - y)

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