Algebra question. How do you solve? Answer is O. [closed]

Calculate value for expression $2(a-2)^2 - 2a(a-3)$ if $a = 4.$ Answer is $0$.

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Do you know how to expand these polynomials? –  Milind May 11 '13 at 9:03
@Utveckla: What's stopping you from being able to solve your problem yourself? –  Hurkyl May 11 '13 at 9:08
What exactly are you looking for here? –  Mike May 11 '13 at 9:09
It looks like she's being asked to simply plug in the value $a = 4$ and do arithmetic.... –  Hurkyl May 11 '13 at 9:10
Since the site is for mathematical questions of any level, it is wrong to say that this is too low level to ask. It is not a well -expressed question because it is not clear precisely what is being asked, or give any context as to what seems to be difficult about the problem. –  Mark Bennet May 11 '13 at 13:08

closed as unclear what you're asking by user1337, Jared, Rick Decker, Daniel Rust, tomaszJul 24 '13 at 1:08

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$$2(a-2)^2 - 2a(a-3)$$ $$2(a^2+4-4a)-(2a^2-6a)$$ $$(2a^2+8-8a)-(2a^2-6a)$$ $$(2a^2+8-8a-2a^2+6a)$$ $$(8-2a)$$ this is the simplest expression.put any value of a and find answer. if a=4 it gives 0.

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Going over the basics. Thanks. –  Utveckla och förenkla May 11 '13 at 9:14
@Utvecklaochförenkla Is this is yours desirable solution?If you face any problem in my solution let me know –  iostream007 May 11 '13 at 9:18

Given: $2(a-2)^2 - 2a(a-3)$ when $a=4$

$2(a-2)^2 - 2a(a-3)$

= $2(4-2)^2 - 2(4)(4-3)$ Substitute $a = 4$

= $2(4-2)(4-2)-8(4-3)$ Expand $(4-2)^2$

= $2(2)(2)-32+24$

= $8-32+24$

= $0$

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$2(a-2)^2-2a(a-3)=0 \quad$ calculate "$+2a(a-3)$"

$2(a-2)^2 = 2a(a-3) \quad$ divide by 2

$(a-2)^2 = a(a-3)$

$(a-2)(a-2) = a^2-3a \quad$ use binomical formula

$a^2-2a-2a+4 = a^2-3a \quad$ calculate $-a^2$ and $+4a$

$4 = a$

It does seem to me to be a distraction to do lots of algebraic manipulation here. Sometimes it helps but the recipe is essentially to put $4$ instead of $a$ wherever $a$ appears in the formula.
So $$2\times(4-2)^2-2\times4\times(4-3)=2\times 4-2\times4\times1=8-8=0$$