To find an expression equivalent to R * S = 6, we first need to substitute the given expressions for Rx and Sx into the equation.
We have:
Rx = 3x + 1
and
Sx = 2x + 1
Now, let’s calculate R * S:
R * S = (3x + 1)(2x + 1)
Next, we multiply the two expressions:
R * S = 3x * 2x + 3x * 1 + 1 * 2x + 1 * 1
This simplifies to:
6x^2 + 3x + 2x + 1
Combining like terms, we get:
6x^2 + 5x + 1
Now we set this equal to 6:
6x^2 + 5x + 1 = 6
Subtracting 6 from both sides gives us:
6x^2 + 5x – 5 = 0
So the expression we’re looking for, equivalent to R * S = 6, is:
6x^2 + 5x – 5 = 0.