Sure! Let's simplify the expression [tex]\((5x - 6.9)(2x + 12.2)\)[/tex] step-by-step.
First, we use the distributive property (also known as the FOIL method for binomials) to expand the product:
1. Multiply the first terms in each binomial:
[tex]\(5x \cdot 2x = 10x^2\)[/tex]
2. Multiply the outer terms in the binomials:
[tex]\(5x \cdot 12.2 = 61x\)[/tex]
3. Multiply the inner terms in the binomials:
[tex]\(-6.9 \cdot 2x = -13.8x\)[/tex]
4. Multiply the last terms in each binomial:
[tex]\(-6.9 \cdot 12.2 = -84.18\)[/tex]
Next, combine all these products:
[tex]\[10x^2 + 61x - 13.8x - 84.18\][/tex]
Combine the like terms ([tex]\(61x\)[/tex] and [tex]\(-13.8x\)[/tex]):
[tex]\[10x^2 + 47.2x - 84.18\][/tex]
So, the simplified form of the expression [tex]\((5x - 6.9)(2x + 12.2)\)[/tex] is:
[tex]\[10x^2 + 47.2x - 84.18\][/tex]
Therefore, the correct answer is:
b. [tex]\(10x^2 + 47.2x - 84.18\)[/tex]
