Question

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

Answer 1

8x³ - 2x² - 51x - 45

Explanation:

(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL

= (x - 3)(8x² + 10x + 12x + 15)

= (x - 3)(8x² + 22x + 15)

multiply each term in the second factor by each term in the first factor.

x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis

= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms

= 8x³ - 2x²- 51x - 45

Answer 2

Expand first 2 bracket first to get:

2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.

2x^2 - 3x - 9 (4x + 5)

2x^2 x 4x = 8x^4

2x^2 x 5 = 10x^2

Repeat for the next two numbers next to the bracket.

You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45

Final simplified answer of:

8x^3 - 2x^2 - 51x - 45

Hope this helps!