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Simplify

[tex]\[
(5x - 6.9)(2x + 12.2)
\][/tex]

A. [tex]\[10x - 84.18\][/tex]
B. [tex]\[10x^2 + 47.2x - 84.18\][/tex]
C. [tex]\[7x^2 + 74.8x + 5.3\][/tex]
D. [tex]\[7x^2 + 5.3\][/tex]

Sagot :

GinnyAnsweridn
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]
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