binomials

What is meant by the 'square of a binomial'?

The square of a binomial is the product of a binomial multiplied by itself. A binomial is an algebraic expression consisting of two terms.

What are the general formulas for squaring a binomial?

The general formulas are:

• For a sum: (a+b)^2 = a^2 + 2ab + b^2
• For a difference: (a-b)^2 = a^2 - 2ab + b^2

Expand the binomial (x+7)^2.

To expand (x+7)^2, use the formula (a+b)^2 = a^2 + 2ab + b^2
Here, a=x and b=7.
So, (x)^2 + 2(x)(7) + (7)^2 = x^2 + 14x + 49

Expand the binomial (3y-4)^2.

To expand (3y-4)^2, use the formula (a-b)^2 = a^2 - 2ab + b^2
Here, a=3y and b=4.
So, (3y)^2 - 2(3y)(4) + (4)^2 = 9y^2 - 24y + 16