Multiply to find answer

Question

(1-6a)(1-7a)=?

Answer 1

Hello.

(1*1)-(6a*1)-(7a*1)+(6a*7a)

1-6a-7a+42a^2

42a^2 - 13a + 1

Answer 2

Traditionally, people will tell you to use the "FOIL" method (First, Outside, Inside, Last).  It works in this situation, but it doesn't if you don't have two binomials. 

I like to think of it as a dance:  each term on the left dances with each term on the right.  Then you combine the "like terms" and there you have it. 

(1)(1) + (1)(-7a) + (-6a)(1) + (-6a)(-7a) yields

1 -7a -6a + 42a^2 = 42a^2 -13a +1 (in descending order)

This works with other types of polynomials.  For example, (2x +1)(x^2 -4x +7):

(multiplied) 2x^3 -8X^2 +14x + 1x^2 -4x +7    (combined) 2x^3 -7x^2 +10x +7

It's just the distributive property, which is not limited to examples such as 3(x +7).  In this case you just have the 3 dancing with the x and the 7.  No difference!