Question

Evaluate the product: $(x+4)(x-4)$

• A. $x^2+8x-16$
• B. $x^2+8x+16$
• C. $x^2+16$
• D. $x^2-16$

Answer 1

The correct option is D $x^2-16$

The product $(x+4)(x-4)$ can be evaluated using Foil method as:

$\underset{–}{Step1:}$
We would multiply the "FIRST" terms of both the brackets given in the product $(x+4)(x-4)$ i.e. $x$ and $x$.


$x\times x=x^2$

The first term of the product $(x+4)(x-4)$ is $x^2$.

$\underset{–}{Step2:}$
Now, we would multiply the "OUTER" terms of the product $(x+4)(x-4)$ i.e. $x$ and $-4$


$x\times (-4)=-4x$

The second term of the product $(x+4)(x-4)$ is $-4x$.

$\underset{–}{Step3:}$
Now, we would multiply the "INNER" terms of the product $(x+4)(x-4)$. (i.e., $4$ and $x$)


$4\times x=4x$

The third term of the product $(x+4)(x-4)$ is $4x$.


$\underset{–}{Step4:}$
Now, we would multiply the "LAST" terms of the product $(x+4)(x-4)$. (i.e., $4$ and $-4$)


$4\times (-4)=-16$
The fourth term of the product $(x+4)(x-4)$ is $-16$.


$\underset{–}{Step5:}$
To find the value of the product $(x+4)(x-4)$, we need to add all the terms.

Product $=$ First term $+$ Second term $+$ Third term $+$ Fourth term

Hence, $(x+4)(x-4)$ is
$=x^2+(-4x)+4x+(-16)$
$=x^2\underset{–}{-4x+4x}-16$
$=x^2-16$

The value of the product $(x+4)(x-4)$ is $x^2-16$.
Therefore, option (d.) is the correct answer.