Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Find the value of c such that each expression is a perfect-square trinomial.
Please show steps on all thank you!
1.  x^2-16x+c
2. p^2-14p+c
3. b^2+18b+c
4. n^2-n+c


Sagot :

[tex](a\pm b)^2=a^2\pm2ab+b^2\\\\1.\ x^2-16x+c=x^2-2x\cdot8+c\to c=8^2=64\\\\x^2-16x+64=x^2-2x\cdot8+8^2=(x-8)^2\\\\\\2.\ p^2-14p+c=p^2-2p\cdot7+c\to c=7^2=49\\\\p^2-14p+49=p^2-2p\cdot7+7^2=(p-7)^2[/tex]


[tex]3.\ b^2+18b+c=b^2+2b\cdot9+c\to c=9^2=81\\\\b^2+18b+81=b^2+2b\cdot9+9^2=(b+9)^2\\\\\\4.\ n^2-n+c=n^2-2n\cdot\frac{1}{2}\to c=(\frac{1}{2})^2=\frac{1}{4}\\\\n^2-n+\frac{1}{4}=n^2-2n\cdot\frac{1}{2}+(\frac{1}{2})^2=(n-\frac{1}{2})^2[/tex]