What Must Be Subtracted From 12k⁴ + 8k³ + 9k² – 12 To Produce 8k⁴ + 8k³ + 2…

What must be subtracted from 12k⁴ + 8k³ + 9k² – 12 to produce 8k⁴ + 8k³ + 25k² – 18k – 16? ​

Answer:

To solve this problem, we need to determine which terms are common to both expressions and which ones are unique to each expression.

The common terms are 8k^3 and 25k^2, since they appear in both expressions. Therefore, we need to subtract the difference of the unique terms from the original expression.

The unique terms in the first expression are 12k^4 and 9k^2, while the unique terms in the second expression are 8k^4, -18k, and -16. To get the difference, we simply subtract the second expression from the first expression:

(12k^4 + 8k³ + 9k² – 12) – (8k^4 + 8k³ + 25k² – 18k – 16)

= 12k^4 – 8k^4 + 8k³ – 8k³ + 9k² – 25k² – (-12k + 18k) – (-12 + 16)

= 4k^4 – 16k² + 6k – 4

Therefore, we need to subtract 4k^4 – 16k^2 + 6k – 4 from 12k^4 + 8k³ + 9k² – 12 to produce 8k^4 + 8k³ + 25k² – 18k – 16.

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What Must Be Subtracted From 12k⁴ + 8k³ + 9k² – 12 To Produce 8k⁴ + 8k³ + 2…

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