Question

How do you write `(5x^2 - 4x + 5) (3x^2 - 6x + 2)` in standard form?

Answer 1

`15x^4-42x^3+49x^2-38x+10`

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This is illustrated below.

`(color(red)(5x^2-4x+5))(3x^2-6x+2)`

`=color(red)(5x^2)(3x^2-6x+2)color(red)(-4x)(3x^2-6x+2)`
`color(white)(xxxx)color(red)(+5)(3x^2-6x+2)`

distributing gives.

`15x^4-30x^3+10x^2-12x^3+24x^2-8x+15x^2-30x+10`

collecting like terms.

`15x^4+(-30-12)x^3+(10+24+15)x^2+(-8-30)x+10`

`=15x^4-42x^3+49x^2-38x+10larr" in standard form"`

Writing in standard form means, start with the term of the highest power of the variable, followed by terms with decreasing powers of the variable.