Question

1. expand the following:

(2x + 3)² - (x² +2x -4)

Explanation:

Step1: Expand \((2x + 3)^2\)

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = 2x\) and \(b = 3\), we get:
\((2x)^2 + 2\times(2x)\times3 + 3^2 = 4x^2 + 12x + 9\)

Step2: Subtract \((x^2 + 2x - 4)\)

Now subtract the second polynomial from the expanded form:
\((4x^2 + 12x + 9) - (x^2 + 2x - 4)\)
Distribute the negative sign:
\(4x^2 + 12x + 9 - x^2 - 2x + 4\)

Step3: Combine like terms

Combine the \(x^2\) terms: \(4x^2 - x^2 = 3x^2\)
Combine the \(x\) terms: \(12x - 2x = 10x\)
Combine the constant terms: \(9 + 4 = 13\)
So we have \(3x^2 + 10x + 13\)

Answer:

\(3x^2 + 10x + 13\)