Question

What is the standard form of `y= (x-3)(x^3-5)-3x^4-5`?

Answer 1

Multiply through and collect like terms to find the solution:

`y=-2x^4-3x^3-5x+10`

Explanation:

`y=(x−3)(x^3−5)−3x^4−5`

Multiply the two sets of brackets using the 'FOIL - firsts, outers, inners, lasts' rule. It's a simple way to ensure that we don't forget any of the necessary multiplications:

`y=(x^4-3x^3-5x+15)−3x^4−5`

Now collect like terms to find the solution:

`y=-2x^4-3x^3-5x+10`

Note that the terms are written in decreasing orders of powers of `x`.