Simplify to create an equivalent expression. -5(1-5k)-4(2k+5) Choose 1 answer: (A) -17 k-25 (B) -17 k+25 (c) 17 k+25 (D) 17 k-25

Distribute -5 and -4: Distribute the -5 across the terms inside the first parentheses and -4 across the terms inside the second parentheses. -5(1-5k) becomes -5*1 + (-5)*(-5k), which simplifies to -5 + 25k. -4(2k+5) becomes -4*2k + (-4)*5, which simplifies to -8k - 20.Combine Step 1 results: Combine the results from Step 1. Combine -5 + 25k and -8k - 20 into a single expression. Expression: -5 + 25k - 8k - 20Combine like terms: Combine like terms in the expression -5 + 25k - 8k - 20. Combine the k terms: 25k - 8k = 17k. Combine the constant terms: -5 - 20 = -25. Expression: 17k - 25

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Simplify to create an equivalent expression.

-5(1-5k)-4(2k+5)
Choose 1 answer:
(A)
-17 k-25
(B)
-17 k+25
(c)
17 k+25
(D)
17 k-25

Simplify to create an equivalent expression. $\newline$ $-5(1-5k)-4(2k+5)$ $\newline$ Choose $1$ answer: $\newline$ (A) $-17 k-25$ $\newline$ (B) $-17 k+25$ $\newline$ (C) $17 k+25$ $\newline$ (D) $17 k-25$

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Math Problems

Algebra 1

Simplify variable expressions involving like terms and the distributive property

Full solution

Q. Simplify to create an equivalent expression.

\newline

-5(1-5k)-4(2k+5)

\newline

Choose

1

answer:

\newline

(A)

-17 k-25

\newline

(B)

-17 k+25

\newline

(C)

17 k+25

\newline

(D)

17 k-25

Distribute $-5$ and $-4$ : Distribute the $-5$ across the terms inside the first parentheses and $-4$ across the terms inside the second parentheses. $\newline$ $-5(1-5k)$ becomes $-5 \times 1 + (-5) \times (-5k)$ , which simplifies to $-5 + 25k$ . $\newline$ $-4(2k+5)$ becomes $-4 \times 2k + (-4) \times 5$ , which simplifies to $-8k - 20$ .
Combine Step $1$ results: Combine the results from Step $1$ . $\newline$ Combine $-5 + 25k$ and $-8k - 20$ into a single expression. $\newline$ Expression: $-5 + 25k - 8k - 20$
Combine like terms: Combine like terms in the expression $-5 + 25k - 8k - 20$ . $\newline$ Combine the $k$ terms: $25k - 8k = 17k$ . $\newline$ Combine the constant terms: $-5 - 20 = -25$ . $\newline$ Expression: $17k - 25$