Question

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

Answer 1

Answer:

2x(5x + 14) + 15

Step-by-step 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