Math problem help?

Question

I keep getting x, but I know its wrong,please walk me through this

Simplify

2x(x-3) + x(5-x)

Answer 1

2x(x - 3) + x(5 - x)

First, let's distribute the 2x over the first brackets.

2x(x) - 2x(3) + x(5 - x)

Now, let's distribute the x over the second brackets.

2x(x) - 2x(3) + x(5) - x(x)

Simplifying, we get

2x^2 - 6x + 5x - x^2

Combining like terms,

2x^2 - x^2 - 6x + 5x

simplifies into

x^2 - x

Answer 2

Answer: x^2-x

Walk Through:

1) 2x(x-3) + x(5-x) Use the distributive property
2x^2 - 6x + 5x - x^2

2) 2x^2 - 6x + 5x - x^2 Group Like-terms
2x^2 - x^2 - 6x + 5x

3) Note: you can only combine terms that are raised to the same power
2x^2 - x^2 - 6x + 5x Combine Like-terms
x^2-x

Hope this helps you.

Answer 3

OK. For this problem, you need to distribute to get:

(2x)(x) + (2x)(-3) + (x)(5) + (x)(-x)

2x^2 - 6x + 5x - x^2

Simplify the expression above and get: (by combining like terms)

x^2 - x

Hope this helps!

Let me know if you have any other questions

- Andrew

Answer 4

X^2 + -X

Answer 5

The result is x^2 - x or x(x - 1).*** (Added note: indeed, I quote below a source indicating that the latter is the final "simplification.") Here's my approach:

2x(x-3) + x(5-x) = x(2x - 6 + 5 - x) = x(x - 1) = x^2 - x.

Note:

1. DON'T expand everything to begin with. Rather, NOTICE that 'x' is a COMMON FACTOR, and retain it outside the parentheses.

2. *** It's arguable whether x^2 - x or x(x - 1) is the (most) "simplified" form. ###

Live long and prosper.

### Added note: Here, from a website calling itself "Highline Advanced Math Program --- A fun math enrichment program for kids in grades 5-7" one finds:
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c. This often lets you simplify an expression by combining the terms inside the parentheses. Here's an example:
1. Start with: 4ac - 2bc + 3ac + 5bc
2. All terms involve c, so we have :(4a - 2b + 3a + 5b)c
3. We can group the a and b terms also:((4 + 3)a + (-2 + 5)b)c
4. Now simplify:( 7a + 3b )c
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Notice that here, "simplification" indeed ends with a FACTORED expression; in our case that would be x(x - 1). Accepting this makes the reason for my first point above clear: 'x' is ALREADY a common factor, so there is no point in not extracting it from both terms from the beginning.

Answer 6

2x(x-3) + x(5-x)

Distributive Property:
2x(x) - 2x(3) + x(5) - x(x)

Simplify terms:
2x^2 - 6x + 5x - x^2

Rearrange:
2x^2 - x^2 + 5x - 6x

Combine like terms:
x^2 - x

Answer 7

2x(x-3) + x(5-x) = 2x^2 -6x + 5x -x
= 2x^2 - 2x
= 2x(x-1)

If the equation = 0, then x = 0 & x = 1

Answer 8

2x(x-3) + x(5-x)
=2x^2 - 6x +5x -x^2
=x^2-x
= x(x-1)

Answer 9

2x(x - 3) + x(5 - x)
Expand the brackets
= 2x² - 6x + 5x - x²
Put like terms together
= x² - x
Can be simplified to x(x - 1)

Answer 10

2x(x-3) + x(5-x)
= 2x^2-6x+5x-x^2
=x^2-x