Apply $(a + b)^2 = a^2 + 2ab + b^2$ with $a = 2.4x$ and $b = 1.1$. Be careful when squaring $2.4$ and $1.1$.

Rewrite the expression as the expanded first quadratic minus the second quadratic. Then distribute the minus sign through each term in the parentheses before combining like terms.

After distributing, group the $x^2$ terms, the $x$ terms, and the constant terms separately, and then add each group.

Type the given expression into Desmos as:

This defines the function you want to match.

Add four more lines for the choices:

• $y_A = 2.16x^2 - 10.56x + 0.4$
• $y_B = -2.16x^2 + 10.56x + 2.02$
• $y_C = 5.76x^2 + 5.28x + 0.4$
• $y_D = 2.16x^2 + 10.56x + 0.4$. Zoom the graph so you can see where the curves lie.

Click on the colored icon next to each function and either:

• Visually check which $y_\text{choice}$ graph lies exactly on top of the original $y$ graph for all visible $x$-values, or
• Use a table (tap the gear icon, then "Convert to table") to compare $y$ and each $y_\text{choice}$ at several $x$-values. The correct choice will match $y$ for every tested $x$.

The expression is a difference of two parts:

First, you should expand the square $(2.4x + 1.1)^2$. Then you will subtract the quadratic in the parentheses.

Use the formula $(a + b)^2 = a^2 + 2ab + b^2$ with $a = 2.4x$ and $b = 1.1$.

• $a^2 = (2.4x)^2 = 5.76x^2$ because $2.4^2 = 5.76$.
• $2ab = 2 \cdot 2.4x \cdot 1.1 = 5.28x$ because $2.4 \cdot 1.1 = 2.64$ and $2 \cdot 2.64 = 5.28$.
• $b^2 = (1.1)^2 = 1.21$.

So

Now rewrite the whole expression using the expanded form:

Distribute the minus sign across the second set of parentheses:

So the expression becomes

Group and combine like terms:

• Quadratic terms: $5.76x^2 - 3.6x^2 = 2.16x^2$.
• Linear terms: $5.28x + 5.28x = 10.56x$.
• Constant terms: $1.21 - 0.81 = 0.4$.

So the simplified expression is

which matches choice D.