Question

Write the following function in standard form. Show your work. y=(x-5)(x+5)(2x-1)

Answer 1

`\boxed{y=4x^3-x^2-50x+25}`

Explanation:

The given function is

`y=(x-5)(x+5)(2x-1)`

Observe that, the first two factors are from difference of two squares.

`\Rightarrow y=(x^2-5^2)(2x-1)`

`\Rightarrow y=(x^2-25)(2x-1)`

We expand the brackets using the distributive property to obtain;

`\Rightarrow y=2x^2(2x-1)-25(2x-1)`

`\Rightarrow y=4x^3-x^2-50x+25`

The above function is now in standard form, since the terms are arranged in descending powers of
`x`.