Question

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

Answer 1

b = 10

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

Answer 2

b = 10

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