Answer :
To simplify the expression [tex]\(-2(p+4)^2 - 3 + 5p\)[/tex], let's go through it step by step.
1. Expand the squared term [tex]\((p+4)^2\)[/tex]:
[tex]\[ (p+4)^2 = p^2 + 8p + 16 \][/tex]
2. Multiply this expanded expression by [tex]\(-2\)[/tex]:
[tex]\[ -2(p^2 + 8p + 16) = -2p^2 - 16p - 32 \][/tex]
3. Now substitute this back into the original expression:
[tex]\[ -2(p+4)^2 - 3 + 5p = -2p^2 - 16p - 32 - 3 + 5p \][/tex]
4. Combine the like terms:
- For the [tex]\(p^2\)[/tex] term:
[tex]\[ -2p^2 \][/tex]
- For the [tex]\(p\)[/tex] terms:
[tex]\[ -16p + 5p = -11p \][/tex]
- For the constant terms:
[tex]\[ -32 - 3 = -35 \][/tex]
5. Combine all terms to write the simplified expression:
[tex]\[ -2p^2 - 11p - 35 \][/tex]
Thus, the simplified expression in standard form is:
[tex]\[ \boxed{-2p^2 - 11p - 35} \][/tex]
So, the correct answer is:
[tex]\[ -2p^2 - 11p - 35 \][/tex]
1. Expand the squared term [tex]\((p+4)^2\)[/tex]:
[tex]\[ (p+4)^2 = p^2 + 8p + 16 \][/tex]
2. Multiply this expanded expression by [tex]\(-2\)[/tex]:
[tex]\[ -2(p^2 + 8p + 16) = -2p^2 - 16p - 32 \][/tex]
3. Now substitute this back into the original expression:
[tex]\[ -2(p+4)^2 - 3 + 5p = -2p^2 - 16p - 32 - 3 + 5p \][/tex]
4. Combine the like terms:
- For the [tex]\(p^2\)[/tex] term:
[tex]\[ -2p^2 \][/tex]
- For the [tex]\(p\)[/tex] terms:
[tex]\[ -16p + 5p = -11p \][/tex]
- For the constant terms:
[tex]\[ -32 - 3 = -35 \][/tex]
5. Combine all terms to write the simplified expression:
[tex]\[ -2p^2 - 11p - 35 \][/tex]
Thus, the simplified expression in standard form is:
[tex]\[ \boxed{-2p^2 - 11p - 35} \][/tex]
So, the correct answer is:
[tex]\[ -2p^2 - 11p - 35 \][/tex]
