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QuestionSimplify: 7p−p2+9p+q2−16−5q2+67p - p^2 + 9p + q^2 - 16 - 5q^2 + 6 and 16p−p2−4q2−1016p - p^2 - 4q^2 - 10.

Studdy Solution

STEP 1

Assumptions1. The expression is given as7p−p+9p+q−16−5q+67 p-p^{}+9 p+q^{}-16-5 q^{}+6. We need to simplify this expression by combining like terms.

STEP 2

First, let's identify the like terms in the expression. Like terms are terms that have the same variables and powers. The like terms in the expression are1. 7p7p and 9p9p - both are terms in pp.
2. −p2-p^{2} - it's the only term in p2p^{2}. . q2q^{2} and −5q2-5q^{2} - both are terms in q2q^{2}.
4. −16-16 and 66 - both are constant terms.

STEP 3

Now, let's combine the like terms. We'll start with the terms in pp.
7p+9p=16p7p +9p =16p

STEP 4

Next, we'll combine the terms in p2p^{2}. Since there's only one term in p2p^{2}, it remains as it is.
−p2=−p2-p^{2} = -p^{2}

STEP 5

Then, we'll combine the terms in q2q^{2}.
q2−5q2=−4q2q^{2} -5q^{2} = -4q^{2}

STEP 6

Finally, we'll combine the constant terms.
−16+6=−10-16 +6 = -10

STEP 7

Now, we'll put all the combined terms together to form the simplified expression.
16p−p2−4q2−1016p - p^{2} -4q^{2} -10So, the simplified expression of7p−p2+9p+q2−16−5q2+67 p-p^{2}+9 p+q^{2}-16-5 q^{2}+6is16p−p2−4q2−1016p - p^{2} -4q^{2} -10

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