Question

Please help me..... I really will appreciate anyone who does help.

Try to show work/explain.

a) If (5x−2)^2=ax^2−bx+c, what is the value of a+c^2?
b)If (3x+5)2=ax2+bx+c, what is the value of a+b+c?

Answer 1

For both problems, expand the left hand side and match up the coefficients.

a.
`(5x-2)^2=25x^2-20x+4=ax^2-bx+c`

`\implies a=25,b=20,c=4`

`\implies a+c^2=25+4^2=41`

b.
`(3x+5)^2=9x^2+30x+25=ax^2+bx+c`

`\implies a=9,b=30,c=25`

`\implies a+b+c=9+30+25=59`