A few days ago
alexie.

factoring-why did my teacher do this?

i just started back to school, so i’m not remembering some things.

we were working on factoring in class, which is a piece of cake, but my teacher showed us to do something i’ve never done before in my work with factoring.

#1 15xy+8+20x+6y

we switched the middle two so it could be factored easier:

15xy+20x+8+6y

5x(3y+4) + 2(4+3y)

(3y+4)(5x+2)

then, he did this on #2

6x^2 +14y-4xy-21x

switched the middle two:

6x^2-4xy+14y-21x

2x(3x-2y) + 7(2y-3x)

he said since the order of the 2y and 3x was different on both sides, you have to swith the sign to make them switch. so:

2x(3x-2y) – 7(3x-2y)

(3x-2y)(2x-7)

i’m not comprehending why he changed the sign on the second one and not the first one.

totally not in school mode yet.

thanks in advance!

Top 1 Answers
A few days ago
Anonymous

Favorite Answer

With the first example, all the signs are +, and therefore therefore you can switch terms around without changing signs at all.

However, in an expression such as

– (a + b – c)

the minus before the bracket changes the sign of every term inside the brackets.

-(a + b – c) = – a – b + c.

Applying the same priciple in reverse:

+ 7(3x – 2y)

= – 7(- 3x + 2y)

Because you have changed the sign of the 7, you must change the sign of every term inside the brackets.

The next step is simply to reverse the terms in the brackets, giving:

– 7(+ 2y – 3x)

and then to remove the superfluous plus sign in front of 2y:

– 7(2y – 3x).

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