Simplify the expression. Write the result using + exponents only.?






first you must use F.O.I.L. method

multiply the firsts, then the outers, then the inners, and then the lasts

1/5x * 1/2x = 1/10x^2

1/5x * -1/4 = -1/20x

1/2 * 1/2x = 1/4x

1/2 * -1/4 = -1/8

so your new expression becomes

1/10x^2 - 1/20x + 1/4x - 1/8

you want to combine like terms, there's only two like terms in here. 1/20x and 1/4x, in order to do that, you must find the lowest common denominator.

so your denominators are 20x and 4x, the lowest common denominator is definitely 20x,

so -1/20x, 20x is already the LCD, so leave that alone,

1/4x, what do you need to do to get an LCD of 1/20x?

you need to multiply top and bottom by 5.

1/4x = 5/20x

so now you have this

1/10x^2 - 1/20x + 5/20x - 1/8

now combine like terms, and you get

1/10x^2 +4/20x - 1/8

4/20x can reduce to 1/5x


1/10x^2 + 1/5x - 1/8

that should be your most simplified answer, however, you can combine all those fractions together, but that would require finding an LCD for all of them.

let's try it anyway. let's combine all the fractions into one big fraction.

your denominators are

10x^2, 5x, and 8

what's your LCD? it's actually 40x^2, do what you need to do to each fraction to get the LCD,

you should get this:

4/40x^2 + 8x/40x^2 - 5x^2/40x^2

combine like terms, and you get

(-5x^2 + 8x + 4)/40x^2

i personally think that this fraction is confusing. but it may be considered simplified to others,

i'm still not sure what the second one is asking, sorry i couldn't help you with that one.


(1/5x+1/2)(1/2x-1/4)= (2x+5)(2x-1)

= 4x^2-2x+10x-5

= 4x^2+8x-5......