Question

final exam - requires respondus lockdown br
started: dec 10 at 8:58pm
quiz instructions
question 21
perform the indicated operation.
$(4x + 3y)^2$
$\circ 4x^2 + 24xy + 9y^2$
$\circ 16x^2 + 24xy + 9y^2$
$\circ 4x^2 + 9y^2$
$\circ 16x^2 + 9y^2$

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 4x\) and \(b = 3y\).

Step2: Calculate \(a^2\)

\(a^2=(4x)^2 = 16x^2\) (since \((ab)^n=a^n b^n\), so \((4x)^2 = 4^2\times x^2=16x^2\)).

Step3: Calculate \(2ab\)

\(2ab = 2\times(4x)\times(3y)=24xy\) (multiply the coefficients and the variables separately).

Step4: Calculate \(b^2\)

\(b^2=(3y)^2 = 9y^2\) (using the same exponent rule as in Step 2).

Step5: Combine the terms

Putting it all together, \((4x + 3y)^2=16x^2 + 24xy + 9y^2\).

Answer:

B. \(16x^{2}+24xy + 9y^{2}\)