(x+2)²=(x+1)² what is the value of A, B, C 

The given equation is:

\[
(x + 2)^2 = (x + 1)^2
\]

To express this in the standard quadratic form \(Ax^2 + Bx + C = 0\), we need to expand both sides and then bring all terms to one side of the equation.

1. Expand both sides:

\[
(x + 2)(x + 2) = x^2 + 4x + 4
\]
\[
(x + 1)(x + 1) = x^2 + 2x + 1
\]

So, the equation becomes:

\[
x^2 + 4x + 4 = x^2 + 2x + 1
\]

2. Subtract the right side from the left side to bring all terms to one side:

\[
(x^2 + 4x + 4) - (x^2 + 2x + 1) = 0
\]

3. Simplify by combining like terms:

\[
x^2 - x^2 + 4x - 2x + 4 - 1 = 0
\]

\[
2x + 3 = 0
\]

This simplifies to a linear equation, but we can still identify the quadratic form where:

\[
0 \times x^2 + 2x + 3 = 0
\]

So, the coefficients \(A\), \(B\), and \(C\) are:

- \(A = 0\)
- \(B = 2\)
- \(C = 3\)

Would you like more details or have any questions?

Here are some related questions:
1. What happens when \(A = 0\) in a quadratic equation?
2. How do you solve the linear equation \(2x + 3 = 0\)?
3. How does the absence of an \(x^2\) term affect the solution of the equation?
4. What are the implications of having \(A = 0\) in the context of quadratic equations?
5. How can you check the solutions of a linear equation?

**Tip:** When simplifying equations, always check whether the highest degree term cancels out; this can indicate that the equation reduces to a simpler form like a linear equation.

Learn how to solve the equation (x + 2)^2 = (x + 1)^2 and find the values of A, B, and C in the standard quadratic form. This problem covers key algebraic concepts, including quadratic equation expansion. Suitable for students in Grades 7-9.

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