4x(3xy + 5y – 8x)] please help?

Question

4x(3xy + 5y – 8x)] show each step of the distribution. Why do you think many students make sign errors on this type of problem? What would be your advice to a student who has trouble with the signs?

Answer 1

4x(3xy + 5y – 8x)

= 4x(3xy) + 4x(5y) – 4x(8x)

= (4*3)(x*x)(y) + (4*5)(x)(y) - (4*8)(x*x)

= 12 x^2 y + 20xy - 32x^2

Now if instead of 4x, you have -4x, then the answer would still be the same except that the signs of each term would change; thus:

= -12 x^2 y - 20xy + 32x^2

Another example:

2x(x - y) - 3y(x - 2y)

= 2(x*x) - 2x(y) - 3y(x) - 3*(-2)(y*y)

= 2x^2 - 2xy - 3xy - (-6)y^2

= 2x^2 - 2xy - 3xy + 6y^2

= 2x^2 - 5xy + 6y^2

Answer 2

= 4x(3xy + 5y - 8x)

= 12x²y + 20xy - 32x²

Answer: 12x²y + 20xy - 32x²

Answer 3

3xy*4x + 5y*4x - 8x*4x

12yx^2 + 20yx - 32x^2

My advice is to write out the multiplication step by step, and put the polynomial portion first (as I did).  Note that I had a "- 8x" times 4x section.

The alternative is to rewrite the original as...

4x(3xy + 5y  + (–8x) )

Eliminate the subtractions by making them additions of negatives.

Answer 4

You have a close bracket without an open bracket.  Not allowed, very confusing in determining operations/orders.

In order to distribute a factor across a polynomial, you multiply the factor by each term (including its sign (+/-)).  So,

(4x)(3xy) + (4x)(5y) + (4x)(-8x) =

Now, that last product looks a little strange with both signs displayed.  After you do this operation (practice,practice,practice), you will see that it is not necessary to use both signs.  Since a positive times a negative is a negative, you can write:

(4x)(3xy) + (4x)(5y) - (4x)(8x) = 12(x^2)y + 20xy - 32x^2

Since there are no like terms to combine, this is the answer.

What are like terms?

Answer 5

12x^2y + 20xy -32x^2

i get my students to make a negative in a red pen so that they dont forget its presence and effect

i also tell them the story of the hubble space telescope that was programmed right here in our hometown by a programmer who missed a negative so that when the telescope got up there it was facing the wrong way!

Answer 6

12y(x^2)+ 20xy - 32(x^2)

I isolated the x into the brackets to show that it's only the "x" that has the "2" power

Answer 7

Shouldn't this be..

=4x(3xy+5y-8x)

=[(4x*3xy)+(4x*5y)-(4x*8x)] <-- this is the step by step

=(12XsquareY+20XY-32Xsquare)

*sorry i typed square because i cannot superscript a 2 here...

Answer 8

4x(3xy + 5y - 8x)

= 4x*3xy + 4x*5y - 4x*8x

= 12x^2y + 20xy - 32x^2

Answer 9

Sign errors are quite common..even for me...At first make them write every step before moving on into the faster BETTER mental calculations...drawing little circle around the "villainous" negative signs are also sometimes helpful....

But let's face the facts...whatever you do...sign errors happen!!!