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If b = a + c and b = 3, then ab + bc =...

If `b = a + c and b = 3`, then `ab + bc = `

A

`sqrt(3)`

B

`3`

C

`3sqrt(3)`

D

`9`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the value of \( ab + bc \) given that \( b = a + c \) and \( b = 3 \). ### Step-by-Step Solution: 1. **Substitute the value of \( b \)**: We know from the problem that \( b = 3 \). Therefore, we can substitute this value into the first equation: \[ b = a + c \implies 3 = a + c \] 2. **Express \( ab + bc \)**: We need to calculate \( ab + bc \). We can factor out \( b \) from this expression: \[ ab + bc = b(a + c) \] 3. **Substitute \( b \) and \( a + c \)**: Now, we substitute \( b = 3 \) and \( a + c = 3 \) (from step 1) into the expression: \[ ab + bc = 3(a + c) = 3 \times 3 \] 4. **Calculate the final value**: Now we can compute the final value: \[ ab + bc = 9 \] Thus, the value of \( ab + bc \) is **9**.
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