(7x+3y)^2
Write it like this:
(7x+3y)(7x+3y)
Our teacher tells us to Foil, which means we multiply the Firsts, the OUters, the Inners, and the Lasts. If you do this, you get
7x(7x) + 7x(3y) + 7x(3y) + 3y(3y)
49x^2 + 21xy + 21xy + 9y^2
49x^2 + 42xy + 9y^2
(a+b)^2=a^2+2*a*b+b^2
(7x+3y)^2=(7x)^2+2*7x*3y+(3y)^2=4+9x^2+42xy+9y^2
Correction:
(7x+3y)^2=(7x)^2+2*7x*3y+(3y)^2=49x^2+42xy+9y^2
To simplify the expression (7x + 3y)^2, we need to apply the concept of squaring a binomial.
When we square a binomial, we multiply it by itself. In this case, we have (7x + 3y) as our binomial. To square it, we need to multiply (7x + 3y) by itself.
To do this, we will use the FOIL method, which stands for First, Outer, Inner, Last. It helps us keep track of the terms we need to multiply. Let's break it down step by step:
First: Multiply the first terms of each binomial.
(7x)^2 = 49x^2
Outer: Multiply the outer terms of each binomial.
(7x) * (3y) = 21xy
Inner: Multiply the inner terms of each binomial.
(3y) * (7x) = 21xy
Last: Multiply the last terms of each binomial.
(3y)^2 = 9y^2
Now, let's put all the terms together:
(7x + 3y)^2 = 49x^2 + 21xy + 21xy + 9y^2
Simplifying further, we can combine like terms:
(7x + 3y)^2 = 49x^2 + 42xy + 9y^2
So, the simplified form of (7x + 3y)^2 is 49x^2 + 42xy + 9y^2.