Question

Which expression is equivalent to the expression below? Select all that apply.

−25(15−20d+5c)

A. −30+40d−10c

B. −6+8d−2c

C. −2c+8d−6

D. 6−8d+2c

Answer 1

After distributing and simplifying −25(15−20d+5c), the equivalent expression is −15+20d−5c, which does not match any of the provided options. Hence, the correct answer is 'None of the above'. Therefore, the correct answer is 'None of the above'.

Step-by-step explanation:

The student's question asks which expressions are equivalent to the given expression −25(15−20d+5c). To find the equivalent expressions, we distribute the −25 across each term inside the parentheses:

• −25 × 15 = −375

• −25 × (−20d) = +500d
• −25 × 5c = −125c

Combining these terms gives us the expression −375+500d−125c. Now, we simplify the expression further by dividing each term by 25:

• −375 ÷ 25 = −15
• 500d ÷ 25 = 20d
• −125c ÷ 25 = −5c

After simplification, the equivalent expression is −15+20d−5c. None of the provided options A. −30+40d−10c, B. −6+8d−2c, C. −2c+8d−6, and D. 6−8d+2c are equivalent to −15+20d−5c. Therefore, the correct answer is 'None of the above'.