multipy (4x+3y)^2

Question

I need help multiplying (4x+3y)^2

I sure appreciate any help! 

Answer 1

First, let's break it up into what it looks like:

(4x + 3y) (4x + 3y)

 

What happens from here is that you multiply the parts in the first parentheses into the second part, so we have:

4x * 4x

4x * 3y

3y * 4x

and 3y * 3y

 

 

4 * 4 = 16,  x * x = x^2,  so 4x * 4x = 16x^2

4 * 3 = 12,  x * y = xy,  so 4x * 3y = 12xy  (and 3y * 4x similarly makes 12xy)

3 * 3 = 9,  y * y =y^2,  so 3y * 3y = 9y^2

 

This means our solution so far is:

16x^2 + 12xy + 12xy + 9y^2

 

Since we have two xy numbers, we can add them together to simplify our final answer to:

16X^2 + 24xy + 9y^2

Answer 2

(4x+3y)^2=(4x+3y)(4x+3y)

(4x+3y)(4x+3y)=(4x)(4x)+(3y)(4x)+(3y)(4x)+(3y)(3y)

16x²+12xy+12xy+9y²=16x²+24xy+9y², or...

(4x+3y)^2=(4x)²+2(4x)(3y)+(3y)²=16x²+24xy+9y²