Question

"factorise
x³ - 25x
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Answer 1

Answer:

"x(x + 5) (x-5)

Step-by-step explanation:

x³ - 25x

= x(x² - 25)

= x(x +5) (x-5) "

Answer 2

STEP

1

:

STEP

2

:

Pulling out like terms

2.1 Pull out like factors :

x3 - 25x = x • (x2 - 25)

Trying to factor as a Difference of Squares:

2.2 Factoring: x2 - 25

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 : 25 is the square of 5

Check : x2 is the square of x1

Factorization is : (x + 5) • (x - 5)

Final result :

x • (x + 5) • (x - 5)