Answer:
b = -2
Step-by-step explanation:
We need to use <u>the binomial theorem</u>, to expand
the expression (3 + bx )⁵ :
(3 + bx )⁵ = 3⁵ + 5(3)⁴(bx)¹ + 10(3)³(bx)² + 10(3)²(bx)³ + 5(3)¹(bx)⁴ + (bx)⁵
= 243 + 5×81×(bx)¹ + 10×27×(bx)² + 10×9×(bx)³ + 5×3×(bx)⁴ + (bx)⁵
= 243 + 405(bx)¹ + 270(bx)² + 90(bx)³ + 15(bx)⁴ + (bx)⁵
= 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵
Then
(3 + bx )⁵ = 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵
Then
The coefficient of x³ in the expansion of (3 + bx )⁵ is 90b³
<u>Comparing the coefficients</u> :
90b³ = -720
Then
b³ = (-720) ÷ 90 = -8
Then
b³ = -8
Then
b = -2
