Will someone please check my answers?
1. Multiply. (a^+2ab-b^2)(a^2-7ab+b^2)
my answer:a^4-5a^3b-14a^2b^2+8ab^3-b^4
2. Simplify. (p^6)^2
________
P^8
my answer:p^4
No, you got the first wrong. Recheck .
Yes on second.
To multiply the expression (a^+2ab-b^2)(a^2-7ab+b^2), you need to use the distributive property and combine like terms. Here's how you can do it step by step:
1. Start by multiplying each term in the first expression (a^+2ab-b^2) by every term in the second expression (a^2-7ab+b^2).
(a^+2ab-b^2) * (a^2-7ab+b^2)
= a^(1+2)*a^2 + a^(1+2)*(-7ab) + a^(1+2)*(b^2)
+ 2ab*a^2 + 2ab*(-7ab) + 2ab*(b^2)
- b^2*a^2 - b^2*(-7ab) - b^2*(b^2)
2. Simplify each term and combine like terms.
= a^3 - 7a^2b + ab^2 + 2a^3b - 14a^2b^2 + 2ab^3 - a^2b^2 + 7ab^3 - b^4
3. Combine like terms to get the final answer.
= a^3 + 2a^3b - 7a^2b + ab^2 - a^2b^2 + 2ab^3 - 14a^2b^2 + 7ab^3 - b^4
Therefore, the correct answer is a^3 + 2a^3b - 7a^2b + ab^2 - a^2b^2 + 2ab^3 - 14a^2b^2 + 7ab^3 - b^4.
For the second question, to simplify (p^6)^2, you need to raise p^6 to the power of 2.
= (p^6)^2
= p^(6*2)
= p^12
Therefore, your answer of p^12 is correct.