Question

What is the standard form of `y= (3x-7)(x-14)(x-11)`?

Answer 1

`3x^3 - 82x^2 + 637x - 1078`

Explanation:

Require to distribute the brackets. Starting with the 1st pair and using FOIL.

`(3x - 7 )(x - 14 ) = 3x^2 - 42x - 7x + 98`

'collecting like terms' gives: `3x^2 - 49x +98`

This now requires to be multiplied by ( x - 11 )

`(3x^2 - 49x +98 )(x - 11 )`
each term in the 2nd bracket requires to be multiplied by each term in the 1st bracket. This is achieved by the following :

`3x^2(x-11) - 49x(x-11) +98(x-11)`

`= 3x^3 - 33x^2 - 49x^2 +539x + 98x - 1078`

writing in standard form means starting with the term with the largest exponent of x and then terms with decreasing terms of exponents.

`rArr 3x^3 -82x^2 + 637x -1078`