Foil Method - Diamond & Melanie

Melanie Mendez & Diamond Valles



The topic we are introducing is the FOIL Method. The FOIL Method is the multiplying of two binomials by distributing twice. FOIL stands for First Outer Inner Last. The meaning of this acronym is the steps used to successfully use the distributive property. First you multiply the outer terms of the binomials. Then you multiply the inner terms of each binomial. After you have gotten your products you combine like terms and you have completely distributed two binomials.

Examples:
1. (3x + 4) (2x-8) -> (3x+4) (2x-8) -> (3x+4) (2x-8) -> (3x+4) (2x-8)
V V V V V V V V
6x^2 + -24x + 8x -32
V
6x^2 + -16x + -32

2. (4x + 2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3)
V V V V V V V V
4x^2 + -12 x + 2x -6
V
4x2+ -10x + -6

3. (2x + 2) (2x +2) -> (2x + 2) (2x + 2) -> (2x + 2) (2x + 2) -> (2x + 2) (2x + 2)
V V V V V V V V
4x2 + 4x + 4x + 4
V
4x2+ 8x + 4

4. (Ax2 + B) (Bx2-C) -> (Ax2 + B) (Bx2 – C) –> (Ax2 + B) (Bx2 – C) –> (Ax2 +B) (Bx2 – C)
V V V V V V V V
ABx2 + _ACx2 + 2Bx2 + -BC
V
ABx2 + -ACx2 + 2Bx2 + -BC

5. (2x+ 2) (x + 2) -> (2x+2) (x+2) -> (2x+2) (x+2) -> (2x+2) (x+2)
V V V V V V V V

2x^2 + 4x + 2x + 4
2x^2 + 6x + 4

Class Examples: 1. (xt5) (x+5)
2. (3x+5) (6x-8)
3. (x+7) (4x-5)
4. (10x-45) (12x+34)
5. (-9c+7) (7c-2)
6. (18d-2) (-12d+7)
7. (x+4) (x-4)
8. (7x + 6) (8x+ 5)
9. (x-5) (9x+5)
10. (10x-10) (10x+10)
Conclusion:

The topic that we are explaining is the FOIL METHOD. The FOIL method consists of multiplying of two binomials by distributing twice. FOIL stands for First Outer Inner Last as we had explained before. The first thing we had done was remember the First Outer Inner Last. For instance, example # 2

2. (4x + 2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3)
V V V V V V V V
4x^2 + -12 x + 2x -6
V
4x^2+ -10x + -6

The fist thing we did was notice the first two numbers in both parentheses. Then we multiplied 4x and x together giving us 4x^2. Then we took the first term from the first parentheses and the second term from the second parentheses and multiplied. Which had given us -12x. Then we took the second term from the first parentheses and the first term from the second parentheses and multiplied, which gave us 2x. We then took the last two terms and multiplied and had gotten -6. Therefore we had gotten 4x^2 + -12x + 2x - 6. Then our final answer is 4x^2 + -10x + - 6. We have introduced the FOIL method in a simple easy way to understand.