Expand and simplify (2x^(2)+3)(4x+5)-8x(x^(2)-2)

Question

Expand and simplify (
`2x^(2)`+3)(4x+5)-8x(
`x^(2)`-2)

Answer 1

2x(5x + 14) + 15

Explanation:

Given: (2
`x^(2)` + 3)(4x + 5) - 8x(
`x^(2)` - 2)

(2
`x^(2)` + 3)(4x + 5) - 8x(
`x^(2)` - 2) = 2
`x^(2)`(4x + 5) + 3(4x + 5) - 8x(
`x^(2)` - 2)

= (8
`x^(3)` + 10
`x^(2)` + 12x + 15) - 8
`x^(3)` + 16x

= 8
`x^(3)` + 10
`x^(2)` + 12x + 15 - 8
`x^(3)` + 16x

collecting like terms to have,

8
`x^(3)`- 8
`x^(3)` + 10
`x^(2)` + 12x + 16x + 15

10
`x^(2)` + 28x + 15

Thus,

(2
`x^(2)` + 3)(4x + 5) - 8x(
`x^(2)` - 2) = 10
`x^(2)` + 28x + 15

= 2x(5x + 14) + 15