Given (2x+b)^2 + c = ax^2 - 4x - 5, find a, b, and c

[girl_in_black]

I know that this is probably really easy, but I have no idea how to do this question ... I would really appreciate it if someone could explain how to solve this:

You're given that

(2x+b)^2 + c = ax^2 - 4x - 5

Calculate the values a, b and c

 

[royhaas]

Expand the left hand side. Then match coefficients of the constant, linear, and quadratic terms.

 

[girl_in_black]

Expand the left hand side. Then match coefficients of the constant, linear, and quadratic terms.

I got as far as multiplying out the left hand side but I don't understand what to do now...
I got 4x^2 + 4xb + b^2 + c = ax^2 - 4x - 5. Is that right?

 

[Mrspi]

Expand the left hand side. Then match coefficients of the constant, linear, and quadratic terms.

I got as far as multiplying out the left hand side but I don't understand what to do now...
I got 4x^2 + 4xb + b^2 + c = ax^2 - 4x - 5. Is that right?

You've expanded correctly. NOW, it was suggested that you should "equate the coefficients." In other words, if the two expressions are to be equal, the coefficients of x<SUP>2</SUP> must be equal, the coefficients of x must be equal, and the constants must be equal.

On the left, the coefficient of x<SUP>2</SUP> is 4. On the right, the coefficient of x<SUP>2</SUP> is a. If the two expressions are equal, then
4 = a

On the left, the coefficient of x is 4b. On the right, the coefficient of x is -4. If the two expressions are equal, then
4b = -4
b = -1

I'll leave it to you to equate the constants and find the value of c (hint: you'll need to use one of the answers we've found already.)

I hope this helps you.

 

[girl_in_black]

That really did help, thank you so much