Return to the original problem. PEMDAS says to multiply before adding. But could you have performed a different operation and still have gotten a correct answer? Which one? Explain.

(4x2 + 8x + 15) + (x2 − x − 27) − (x + 5)(x − 7)

Question

Return to the original problem. PEMDAS says to multiply before adding. But could you have performed a different operation and still have gotten a correct answer? Which one? Explain.

(4x2 + 8x + 15) + (x2 − x − 27) − (x + 5)(x − 7)

Grande03 · Answer

It would be okay to take the second quadratic trinomial out of parentheses and simplify the trinomial addition before multiplying the binomials. As long as we multiply the binomials before subtracting their product, we’re still using the order of operations correctly.

(4x2 + 8x + 15) + (x2 − x − 27) − (x + 5)(x − 7) 	
= 4x2 + 8x + 15 + x2 − x − 27 − (x + 5)(x − 7)

= 4x2 + x2 + 8x − x + 15 − 27 − (x + 5)(x − 7)

= 5x2 + 7x − 12 − (x + 5)(x − 7)

= 5x2 + 7x − 12 − (x2 − 7x + 5x − 35)

= 5x2 + 7x − 12 − (x2 − 2x − 35)

= 5x2 + 7x − 12 − x2 + 2x + 35

= 5x2 − x2 + 7x + 2x − 12 + 35

= 4x2 + 9x + 23

AZ · Answer

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You are absolutely correct! You could add the two trinomials first and it wouldn't change the final answer as long as you multiplied the other two polynomials before finding the difference