I learned multiplying two binomials this week. When there are two terms in a polynomial, it is called binomial. Like these —> 5+x, x-3, y+9, 3y-60x, 9ab-5b
What I’m going to talk about now is multiplying two binomials.
- For example: (3x+1)(4+x)
We can determine the product of this in four ways. I will show all four.
FIRST WAY
We can determine the product by using FOIL.
F – first term in each bracket
O – outside term
I – inside term
L – last term in each bracket
SECOND WAY
We can determine the product by using distributive property.
What we need to do is multiply the first term in the first binomial by the terms in the second binomial, multiply the second term in the first binomial by the terms in the second binomial.
THIRD WAY
We can determine the product by using algebra tiles.
Those are our algebra tiles. Now all we have to do is to place the two binomials that we will multiply, just like in the multiplication table.
The top 3 rectangles represent 3x, so each x represents a rectangle and the square represents 1. The 4 squares on the left represent 4, so each square represents 1, and the rectangle represents x. Now all we have to do is draw the algebra squares from the beginning to the tip of the algebra squares on the top and side. Finally, we will add or subtract the resulting algebra tiles according to the polynomial.
FOURTH WAY
We can determine the product by using area diagram.
This way is just like algebra tiles. We only use shapes in algebra tiles, here we use numbers and variables. What we need to do is to multiply the ones on the top by the ones on the left, just like in the multiplication table.
- Another example: (+)(–)
Now all you have to do is choose the easiest path for you and determine the product of these two binomials.
The easiest way for me is the first way, FOIL. So I’ll do it that way.