If $a+b=20$ and $a-b=6$, then what is $a\times b$?

The correct option is 91.

We are given two algebraic equations:

1. $a+b=20$

2. $a-b=6$

We need to find the value of $a\times b$.

Method 1: Solving for individual variables

Add equation (1) and equation (2) together:

$(a+b)+(a-b)=20+6$

$2a=26$

$a=13$

Now, substitute the value of $a=13$ back into equation (1):

$13+b=20$

$b=20-13$

$b=7$

Now, calculate the product $a\times b$:

$a\times b=13\times 7=91$

Method 2: Using an Algebraic Identity

We can also use the algebraic identity:

$(a+b{)}^2-(a-b{)}^2=4ab$

Substitute the given values into the identity:

$(20{)}^2-(6{)}^2=4ab$

$400-36=4ab$

$364=4ab$

$ab=\frac{364}{4}$

$a\times b=91$

Thus, the value of $a\times b$ is 91.