Question

A rectangle has dimensions 3x+5 and x+7 write an expression for the area the rectangle as a product and as a polynomial in standard form

Answer 1

A = L * W
(3x + 5)(x + 7) = 0
FOIL
3x^2 + 21x + 5x + 35
Combine like terms
3x^2 + 26x + 35 = 0

Answer 2

So the equation to find the area of a rectangle is l=lw
What we want to do is multiply both of the given dimensions to get the area.

(3x + 5)(x + 7)

If you don't know how to multiply polynomials, what you do is multiply the coefficients, and add the exponents of the variables that you're multiplying.

You're first multiplying 3x by both the terms in the second binomial, adding the exponents and multiplying the coefficients

(3x + 5)(x + 7)
(3x + 5)(x + 7) = 3x^2
(3x + 5)(x + 7) = 3x^2 + 21x


Next you're going to move on the the 5, and multiply it by both terms in the second binomial.

(3x + 5)(x + 7) = 3x^2 + 21x
(3x + 5)(x + 7) = 3x^2 + 21x + 5x
(3x + 5)(x + 7) = 3x^2 + 21x + 5x + 35

Combine like terms,

21x + 5x
26x

Therefore, your final trinomial in standard form is
3x^2 + 26x + 35

Hope this helps!
Let me know if there's anything you don't understand and I'll try to explain it as best I can.