Question

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

Answer 1

Answer:

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

Step-by-step 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 $x$.