To multiply binomials using area method and distribution method.
Let's take the binomials:
(x + 4) and (x + 5)
Area Method:
Using area method, let's assume area of a rectangle which is Length x Width.
Let length = (x + 4)
Width = (x + 5)
(x + 4)(x + 5)
Let's take the rectangle below:
How we got value inside the box:
x*x = x²
x*5 = 5x
4*x = 4x
4*5 = 20
Now, write sum up the values inside the box:
x² + 5x + 4x + 20
= x² + 9x + 20
Using distributive method:
(x + 4)(x+5)
Use distributive property, we have:
Distribute the x in the first binomial to the second, also distribute the 4 in the first binomial to the second.
x(x + 5) + 4(x + 5)
= x*x + x*5 + 4*x + 4*5
= x² + 5x + 4x + 20
= x² + 9x + 20