Question

Factorise x^2-16x+64

quickly please

Answer 1

`(x-8)^(2)`

Explanation:

Quadratic expression:

`x^(2) - 16x + 64`

Where

a = 1

b = -16

c = 64

Quadratic expression can be factorized using the Double Bubble Method

Double Bubble Method:

Step 1:

Multiply a and c

a×c = 1 × 64
= 64

Step 2:

Write a complete list of pairs of factors of ac and choose the most appropriate and suitable pair of factors that would add or subtract to equal to the value of b =
`-16`. Accordingly assign the signs to the two factors

Pair of factors:
`-8` and
`-8`

Step 3:

Use the two factors to rewrite the bx term:

`x^(2) - 8x -8x + 64`

Step 4:

Factorize by Grouping:

`x(x-8) -8(x - 8)`

Step 5:

Extract the common factor expression
`(x - 8)` to obtain double-bubble expressions:

`(x - 8)(x-8)`

Step 6:

Apply the Law of indices:

`a^(n)` ×
`a^(m)` =
`a^(n + m)`

∴
`(x-8)^(1)` ×
`(x-8)^(1)` =
`(x-8)^(1+1)`

=
`(x-8)^(2)`

Answer 2

Factor using the perfect square rule.

(x−8)^2

Explanation:

hope this helps