Question

Multiply. $$(x+7 y)^{2}$$

Short answer

The expanded form of the binomial expression (x+7y)^2 is x^2 + 14xy + 49y^2.

Step-by-step solution

Identify the terms in the binomial

In the binomial (x+7y)^2, the terms are x and 7y. Now, these can be related to a and b, as required for the formula of the square of a binomial (a+b)^2 = a^2 + 2ab + b^2.

Apply the binomial square expansion formula

Applying the formula to the binomial (x + 7y)^2 yields x^2 + 2*(x)*(7y) + (7y)^2.

Simplify the equation

Simplifying the equation gives x^2 + 14xy + 49y^2.