Find the product of (x+6)(2x−3)

Question

(__)x^2 +(__)x-(___)

Answer 1

To find the product of \((x+6)(2x-3)\), we can use the distributive property (often referred to as the FOIL method for binomials).

1. First: Multiply the first terms: \[ x \cdot 2x = 2x^2 \]

2. Outer: Multiply the outer terms: \[ x \cdot (-3) = -3x \]

3. Inner: Multiply the inner terms: \[ 6 \cdot 2x = 12x \]

4. Last: Multiply the last terms: \[ 6 \cdot (-3) = -18 \]

Now, combine all these results: \[ 2x^2 - 3x + 12x - 18 \]

Combine like terms (\(-3x + 12x\)): \[ 2x^2 + 9x - 18 \]

Thus, the final product is: \[ 2x^2 + 9x - 18 \]

So filling in the blanks: \[ (2)x^2 + (9)x - (18) \]