What is the product of 6,x^(2)-3x, and x-10? Choose 1 answer: (A) -42 x+180 (B) 6x^(2)-78 x+180 (C) 6x^(3)-42x^(2)+180 x (D) 6x^(3)-78x^(2)+180 x Show calculator

Distribute Terms: Distribute each term in the first polynomial by each term in the second polynomial. We will use the distributive property (a(b + c) = ab + ac) to multiply the two polynomials. (6x^2 - 3x) * (x - 10) = 6x^2 * x + 6x^2 * (-10) - 3x * x - 3x * (-10)Perform Multiplication: Perform the multiplication for each term. 6x^2 * x = 6x^3 6x^2 * (-10) = -60x^2 -3x * x = -3x^2 -3x * (-10) = 30x Now, combine these results: 6x^3 - 60x^2 - 3x^2 + 30xCombine Like Terms: Combine like terms. -60x^2 and -3x^2 are like terms, so we add them together: -60x^2 - 3x^2 = -63x^2 Now the expression is: 6x^3 - 63x^2 + 30xMatch Result: Match the result with the given options. The result from Step 3 is 6x^3 - 63x^2 + 30x, which matches option (C) 6x^3 - 42x^2 + 180x.

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

Q. What is the product of

\newline

6,x^{2}-3x

, and

x-10

\newline

Choose

1

answer:

\newline

(A)

-42x+180

\newline

(B)

6x^{2}-78x+180

\newline

(C)

6x^{3}-42x^{2}+180x

\newline

(D)

6x^{3}-78x^{2}+180x

\newline

Distribute Terms: Distribute each term in the first polynomial by each term in the second polynomial. $\newline$ We will use the distributive property $a(b + c) = ab + ac$ to multiply the two polynomials. $\newline$ $(6x^2 - 3x) * (x - 10) = 6x^2 * x + 6x^2 * (-10) - 3x * x - 3x * (-10)$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $6x^2 \times x = 6x^3$ $\newline$ $6x^2 \times (-10) = -60x^2$ $\newline$ $-3x \times x = -3x^2$ $\newline$ $-3x \times (-10) = 30x$ $\newline$ Now, combine these results: $\newline$ $6x^3 - 60x^2 - 3x^2 + 30x$
Combine Like Terms: Combine like terms. $\newline$ $-60x^2$ and $-3x^2$ are like terms, so we add them together: $\newline$ $-60x^2 - 3x^2 = -63x^2$ $\newline$ Now the expression is: $\newline$ $6x^3 - 63x^2 + 30x$
Match Result: Match the result with the given options. $\newline$ The result from Step $3$ is $6x^3 - 63x^2 + 30x$ , which matches option (C) $6x^3 - 42x^2 + 180x$ .