Hello!
The answer is:
The third option is the correct option.
[tex](y+4)^{2}=22=y^{2}+8y-6[/tex]
Why?
To find the correct answer, we need to expand the notable product of the given choices, and then, compare it to the given expression.
Also, we must remember how to expand the following notable product:
[tex](a+-b)^{2}=a^{2}+-2*ab+b^{2}[/tex]
We are looking for the following expression:
[tex]y^{2}+8y-6=0[/tex]
So, solving we have:
First option:
[tex](y+4)^{2}=10\\\\y^{2}+2*4y+4^{2} =10\\\\y^{2}+8y+16=10\\\\y^{2}+2*4y+16-10=0\\\\y^{2}+2*4y+6=0[/tex]
Hence, we know that the first option is not the correct option.
Second option:
[tex](y-4)^{2}=10\\\\y^{2}-2*4y+4^{2}=28\\\\y^{2}-8y+16=28\\\\y^{2}-8y+16-28=0\\\\y^{2}-8y-12=0[/tex]
Hence, we know that the second option is not the correct option.
Third option:
[tex](y+4)^{2}=22\\\\y^{2}+2*4y+4^{2} =22\\\\y^{2}+8y+16=22\\\\y^{2}+2*4y+16-22=0\\\\y^{2}+8y-6=0[/tex]
Hence, we know that the third option is the correct option.
Have a nice day!
