Use the box method to distribute and simplify (-1+2x)(4+5x).. Drag and drop the terms to the correct locations of the table.

This is very difficult to do without a picture, so hopefully you can follow this explanation

Draw a square box, then cut it in 1/2 vertically and horizontally so you have 4 smaller squares inside the box (Put in the given terms, outside of the box as shown below).

-5x      -3

x     |          |          |

-5    |          |          |

Now multiply the two outside terms that create the intersection to fill in the box. So

Upper left = -5x2 this is the first term of the polynomial

Upper right = -3x this term and the next term make up the middle term

Lower left = 25x and need to be added together = 22x

Lower right = 15 this is the last term in the polynomial

so your answer should be: -5x2 + 22x + 15

Hopefully this helps you!

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb