181k views
4 votes
Show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x

User Pagetribe
by
3.8k points

1 Answer

3 votes

Answer:

see explanation

Explanation:

Given

(2x + 3)³

= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL

= (2x + 3)( 4x² + 12x + 9)

= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis

= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms

= 8x³ + 36x² + 54x + 27

User Angelene
by
3.6k points