(2+(1)/(3)d)(5d+(1)/(3)d^(2)) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) 2+2d^(2) (B) 2+(16)/(3)d+(1)/(3)d^(2) (c) 2+(5)/(3)d^(2)+(1)/(9)d^(3) (D) 10 d+(7)/(3)d^(2)+(1)/(9)d^(3)

Apply Distributive Property: First, we will apply the distributive property (also known as the FOIL method for binomials) to multiply the two expressions. (2+(1)/(3)d)(5d+(1)/(3)d^(2)) = 2*(5d) + 2*((1)/(3)d^(2)) + (1)/(3)d*(5d) + (1)/(3)d*((1)/(3)d^(2))Perform Multiplication: Now, we will perform the multiplication for each term. 2*(5d) = 10d 2*((1)/(3)d^(2)) = (2/3)d^(2) (1)/(3)d*(5d) = (5/3)d^(2) (1)/(3)d*((1)/(3)d^(2)) = (1/9)d^(3)Combine Like Terms: Next, we will combine like terms. 10d + (2/3)d^(2) + (5/3)d^(2) + (1/9)d^(3)Add Coefficients: Adding the coefficients of the d^2 terms: (2/3)d^(2) + (5/3)d^(2) = (2/3 + 5/3)d^(2) = (7/3)d^(2)Simplified Expression: Now, we have the simplified expression: 10d + (7/3)d^(2) + (1/9)d^(3)Compare with Options: We compare the simplified expression with the given options to find the match. The correct option is (D) 10d + (7/3)d^(2) + (1/9)d^(3).

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(2+(1)/(3)d)(5d+(1)/(3)d^(2))
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A)
2+2d^(2)
(B)
2+(16)/(3)d+(1)/(3)d^(2)
(c)
2+(5)/(3)d^(2)+(1)/(9)d^(3)
(D)
10 d+(7)/(3)d^(2)+(1)/(9)d^(3)

$\left(2+\frac{1}{3} d\right)\left(5 d+\frac{1}{3} d^{2}\right)$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2+2 d^{2}$ $\newline$ (B) $2+\frac{16}{3} d+\frac{1}{3} d^{2}$ $\newline$ (C) $2+\frac{5}{3} d^{2}+\frac{1}{9} d^{3}$ $\newline$ (D) $10 d+\frac{7}{3} d^{2}+\frac{1}{9} d^{3}$

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Algebra 1

Compare linear and exponential growth

Full solution

\left(2+\frac{1}{3} d\right)\left(5 d+\frac{1}{3} d^{2}\right)

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

2+2 d^{2}

\newline

(B)

2+\frac{16}{3} d+\frac{1}{3} d^{2}

\newline

(C)

2+\frac{5}{3} d^{2}+\frac{1}{9} d^{3}

\newline

(D)

10 d+\frac{7}{3} d^{2}+\frac{1}{9} d^{3}

Apply Distributive Property: First, we will apply the distributive property (also known as the FOIL method for binomials) to multiply the two expressions. $\newline$ $(2+\frac{1}{3}d)(5d+\frac{1}{3}d^{2}) = 2\cdot(5d) + 2\cdot\left(\frac{1}{3}d^{2}\right) + \frac{1}{3}d\cdot(5d) + \frac{1}{3}d\cdot\left(\frac{1}{3}d^{2}\right)$
Perform Multiplication: Now, we will perform the multiplication for each term. $\newline$ $2\times(5d) = 10d$ $\newline$ $2\times\left(\frac{1}{3}d^{2}\right) = \frac{2}{3}d^{2}$ $\newline$ $\frac{1}{3}d\times(5d) = \frac{5}{3}d^{2}$ $\newline$ $\frac{1}{3}d\times\left(\frac{1}{3}d^{2}\right) = \frac{1}{9}d^{3}$
Combine Like Terms: Next, we will combine like terms. $10d + \left(\frac{2}{3}\right)d^{2} + \left(\frac{5}{3}\right)d^{2} + \left(\frac{1}{9}\right)d^{3}$
Add Coefficients: Adding the coefficients of the $d^2$ terms: $\newline$ $\frac{2}{3}d^{2} + \frac{5}{3}d^{2} = \left(\frac{2}{3} + \frac{5}{3}\right)d^{2} = \frac{7}{3}d^{2}$
Simplified Expression: Now, we have the simplified expression: $10d + \left(\frac{7}{3}\right)d^{2} + \left(\frac{1}{9}\right)d^{3}$
Compare with Options: We compare the simplified expression with the given options to find the match. $\newline$ The correct option is (D) $10d + \frac{7}{3}d^{2} + \frac{1}{9}d^{3}$ .