Question

Subtract. (x^2+43x+10)−(−10x^2−5x+10) Express the answer in standard form. Enter your answer in the box.

Answer 1

(x^2 + 43x +10) - (−10x^2−5x+10)
x^2 + 43x +10 + 10x^2 + 5x - 10
11x^2 + 48x

Answer 2

`(x^2+43x+10)-(-10x^2-5x+10)=11x^2+48x`

Explanation:

Given polynomial
`(x^2+43x+10) \ and \(-10x^2-5x+10)`

We have to subtract the given polynomials.

Consider
`(x^2+43x+10) \ and \(-10x^2-5x+10)`

Subtract (1) - (2) , we have,

`(x^2+43x+10)-(-10x^2-5x+10)`

rewrite by applying plus-minus rule
`-(-a)=a` , we have,

`x^2+43x+10+10x^2+5x-10`

Grouping like terms, (like term are terms with same variable having same degree)

`=x^2+10x^2+43x+5x+10-10`

`\mathrm{Add\:similar\:elements:}\:43x+5x=48x`

`=x^2+10x^2+48x+10-10`

`\mathrm{Add\:similar\:elements:}\:x^2+10x^2=11x^2`

`=11x^2+48x+10-10`

Solving , we get,

`=11x^2+48x`

Thus,
`(x^2+43x+10)-(-10x^2-5x+10)=11x^2+48x`