Question

simplify the following expression.
$(4x + 1)^2$
$16x^2 + ?x + \square$

Explanation:

Step1: Recall the square of a binomial formula

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 4x\) and \(b = 1\).

Step2: Calculate the middle term

For the middle term \(2ab\), substitute \(a = 4x\) and \(b = 1\): \(2\times(4x)\times1 = 8x\).

Step3: Calculate the constant term

For the constant term \(b^2\), substitute \(b = 1\): \(1^2 = 1\).

Answer:

The middle term is \(8\) and the constant term is \(1\), so the simplified expression is \(16x^2 + 8x + 1\). The value for the green box (the coefficient of \(x\)) is \(8\), and the value for the white box (the constant term) is \(1\).