SUBTRACTING ALGEBRAIC EXPRESSIONS

One property of Algebra that hold is the subtraction of expressions. This is by simplifying the given expression. It can be form by monomial, binomial or polynomials. Based on the photo provided, it is by subtracting a binomial from binomial. It actually doesn't matter how the expressions appear. It's the operation on signs does. We both know that multiplying same signs results to positive (+) sign, and (-) for the unlike signs. That mastery leaves us easiness in dealing with the subject matter about expressions. See illustration below.

Given that, -2(-3), this is clearly means that (-)(-)=(+), and (2)(3) = 6. Or this can be +6. For an example like -3(x-4), this is simply mean -3x+12 as direct solution. In similar manner, all of the expressions treated the same.

More illustrations:

Simplify the following:

$1.)3(-{\color{Blue} x})=-3{\color{Blue} x}$ , this is by direct solution.

$2.)-4({\color{Blue} x}-3{\color{Red} y}+2)=-4{\color{Blue} x}+12{\color{Red} y}-8$ , this is by direct solution.

$3.)(5x-2)-(3x-7)=$ , here we want to do it one by one.

$5x-2-(3x-7)=$ , notice that we removed the parenthesis of the first binomial.

$5x-2{\color{Red} -}3x{\color{Red} +}7=$ , now we apply the + and - rules for the second binomial.

$5x{\color{Red} -}3x-2{\color{Red} +}7=$ , gather like terms, 5x and -3x are like terms.

$2x{\color{Red} +}5$ , this is the final answer.

$4.) -(2x+y)-(2y-3)=$ , here we want to do it one by one from the given.

$-2x-y-(2y-3)=$ ,applying the rules for + and - as we remove the parenthesis for the first binomial.

$-2x-y-2y+3=$ ,now we apply the + and - rules for the second binomial.

$-2x-3y+3=$ , we combine -y and -2y as like terms as -3y.

$-2x-3y+3$ , this is also our final answer.

$5.)-2(2x-3y)-(4y+y)=$ , given

$4x+6y-4y-y=$ , removing parenthesis and collect like terms.

$4x+y=$ , combining like terms for y.

$4x+y$ , our final answer.

More examples:

$Simplify.$

$1.) (2x-3y)-x=$

$2x-3y-x=$

$x-3y$ , Answer

$2.)-7(3x-y+2z)-(x+2y)=$

$-21x+7y-14z-x-2y=$

$-21x-x+7y-2y-14z=$

$-22x+5y-14z$ , Answer

$3.)(4a-3b)-(2a+3b)=$

$4a-3b-2a-3b=$

$4a-2a-3b-3b=$

$2a-6b$ , Answer

$4.)-(a-3b)-(2a+b)=$

$-(a-3b)-(2a+b)=$

$-a+3b-2a-b=$

$-a-2a+3b-b=$

$-3a+2b$ , Answer

$5.)(5m-2m+p)-(2m-3n+2p)=$

$5m-2n+p-2m+3n-2p=$

$5m-2m-2n+3n+p-2p=$

$3m+n-p$ , Answer

$6.)(3ab-5cd)-(2dc+ab)=$

$3ab-5cd-2dc-ab=$

$3ab-ab-5cd-2dc=$

$2ab-7cd$ , Answer

$7.)(5ac+2a-3c)-(c+5a-2ac)=$

$5ac+2a-3c-c-5a+2ac=$

$5ac+2ac+2a-5a-3c-c=$

$7ac-3a-4c$ , Answer

$8.)-5(2mn-op+7qr)-3(mn+3op-4qr)=$

$-10mn+5op-35qr-3mn-9op+12qr=$

$-10mn-3mn+5op-9op-35qr+12qr=$ $-10mn-3mn+5op-9op-35qr+12qr=$

$-13mn-4op-23qr$ , Answer

$9.) (2x^{2}-5ay^{2})-(2a^{2}y+3x^{2})=$

$2x^{2}-5ay^{2}-2a^{2}y-3x^{2}=$

$2x^{2}-3x^{2}-5ay^{2}-2a^{2}y=$

$-x^{2}-5ay^{2}-2a^{2}y$ , Answer

$10.)(a-3)-(b-2)-(c-1)=$

$a-3-b+2-c+1=$

$a-b-c-3+2+1=$

$a-b-c$ , Answer

Extra exercises:

Given the expressions, subtract the first from the second expression. Write your answer on a "Post a comment" box found below this page.

$1.)(7x-y),(5y+7)$

$2.)-7(3a-4b+8),(10-6a)$

$3.)7x-3y+z,3y+5x-9z$

PDF worksheet with key found here!!

More PDF with key here

Reference

DMG