\n
![\"\"](\"\/..\/distr.png\")
\nWe see that we take the outer number (in this case, 3) and multiply it by each term in the brackets, writing the result each time.<\/p>\n
In\u00a0math, the distributive property is used\u00a0constantly.\u00a0\u00a0An illustration:<\/p>\n
3(5x-7)=15x-21<\/p>\n
To see what’s really happening here, look to the following:
\n
\nWe see that we take the outer number (in this case, 3) and multiply it by each term in the brackets, writing the result each time.<\/p>\n
A binomial is a couple of terms that cannot be added. In the above example, 5x-7 is a binomial. When two binomials are multiplied together, it might look like this:<\/p>\n
![\"\"](\"\/..\/binoms.png\")
<\/p>\n
In order to multiply a binomial by a binomial, notice the steps below:
\n![\"\"](\"\/..\/foil.png\")
<\/p>\n
(The letters stand for First, Outer, Inner, Last: hence the acronym FOIL)<\/p>\n
F: 2x times 4x gives 8x2<\/span><\/sup> Writing the terms consecutively, we get<\/p>\n 8x2<\/span><\/sup> + 18x -20x -45<\/p>\n Now, we can combine the 18x with the -20x to finally obtain<\/p>\n 8x2<\/span><\/sup> -2x -45.<\/p>\n Indeed, (2x-5)(4x+9) = 8x2<\/span><\/sup> -2x -45.<\/p>\n To verify the FOIL method, try it on (12)(10), written as<\/p>\n (10 +2)(9 + 1)<\/p>\n F: 10(9)=90 90 + 10 + 18 + 2 = 120, which of course we know is the answer to (12)(10).<\/p>\n Hope this helps.<\/p>\n
\nO: 2x times 9 gives 18x
\nI: -5 times 4x gives -20x
\nL: -5 times 9 gives -45<\/p>\n
\nO: 10(1)=10
\nI: 2(9)=18
\nL: 2(1)=2<\/p>\n