Question

2. Factorise: a5 - 16a​

Answer 1

Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a5" was replaced by "a^5".

STEP

1

:

STEP

2

:

Pulling out like terms

2.1 Pull out like factors :

a5 - 16a = a • (a4 - 16)

Trying to factor as a Difference of Squares:

2.2 Factoring: a4 - 16

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 : 16 is the square of 4

Check : a4 is the square of a2

Factorization is : (a2 + 4) • (a2 - 4)

May It help u .......