- #1
educatingrob
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Im completing Engineering Maths cover to cover in an attempt to get more familiar with maths as I finished my education many years ago without really understanding many basic maths concepts. This problem is at the back of the introduction to algebra.
(x-2y)^2 - (2x - y)^2
Now I can expand fairly easily:
x(x-2y) - 2y(x-2y) - (2x)(2x-y) - (-y)(2x-y)
x^2 - 2yx - 2yx + 4y^2 - 4x^2 ... Hmm
I know the rest as its in the book but I don't know the correct method for determining:
- (-y)(2x-y)
because of the negative at the front. without it, its easy:
-y * 2x = -2xy
-y * -y = y^2
thus:
-2xy + y^2
but then you have ... - -2xy + y^2
minus minus?
What I don't understand is how the negative before the brackets affects the result. When expanding is it:
- (-y)(2x-y)
-y * 2x = -2xy * -1 = 2xy
-y * -y = y^2 * -1 = -y^2
or maybe the - term belongs to all the last bit?
- (-2xy + y^2)
so its
-1 * (-2xy + y^2)
= +2xy - y^2
If someone could explain the rule dictated to expand when there's a negative, I would be grateful as I can't find an example or comment about how to think of this.
Of course there's the other FILO way (a+b)(c+d) = ac+bc+bd+ad
but that's just confusing me more WRT expanding the two elements of (x-2y)^2 - (2x - y)^2 because of the negative.
My maths is riddled with these inconsistencies where I just used to guess without understanding what's missing or what rule to follow.
(apologies for the stupid question, thanks for any help)
(x-2y)^2 - (2x - y)^2
Now I can expand fairly easily:
x(x-2y) - 2y(x-2y) - (2x)(2x-y) - (-y)(2x-y)
x^2 - 2yx - 2yx + 4y^2 - 4x^2 ... Hmm
I know the rest as its in the book but I don't know the correct method for determining:
- (-y)(2x-y)
because of the negative at the front. without it, its easy:
-y * 2x = -2xy
-y * -y = y^2
thus:
-2xy + y^2
but then you have ... - -2xy + y^2
minus minus?
What I don't understand is how the negative before the brackets affects the result. When expanding is it:
- (-y)(2x-y)
-y * 2x = -2xy * -1 = 2xy
-y * -y = y^2 * -1 = -y^2
or maybe the - term belongs to all the last bit?
- (-2xy + y^2)
so its
-1 * (-2xy + y^2)
= +2xy - y^2
If someone could explain the rule dictated to expand when there's a negative, I would be grateful as I can't find an example or comment about how to think of this.
Of course there's the other FILO way (a+b)(c+d) = ac+bc+bd+ad
but that's just confusing me more WRT expanding the two elements of (x-2y)^2 - (2x - y)^2 because of the negative.
My maths is riddled with these inconsistencies where I just used to guess without understanding what's missing or what rule to follow.
(apologies for the stupid question, thanks for any help)