Question

The expression (2x + a)(4x − 1) is equivalent to 8x2+ bx − 3. Find the value of b.

Answer 1

Answer:

b = 10

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms

(2x + a)(4x - 1) ← expand using FOIL

= 8x² + 4ax - 2x - a = 8x² + x(4a - 2) - a

Compare coefficients of like terms with

8x² + bx - 3

Then a = 3 ( constant term )

b = 4a - 2 ( coefficients of the x- term )

b = 4(3) - 2 = 12 - 2 = 10

Answer 2

Answer:

b = 10

Step-by-step explanation:

We can break those parenthesis like this

$(2x + a)(4x - 1) \\ = 2x(4x - 1) + a(4x - 1) \\ = 8{x}^{2} - 2x + 4ax - a$

And then combine the terms end with x we get

$8 {x}^{2} - 2x + 4ax - a \\ = 8 {x}^{2} + 4ax - 2x - a \\ = 8 {x}^{2} + (4a - 2)x - a$

Now by comparing 2 expressions, we can see that a is 3, and b = 4a-2 = 12-2 = 10