Question

Bradley has 3 square pieces of cardboard with each side equal to x units. For each piece, he does something different to it according to each part below:

Part A: Bradley pasted rectangular strips along two adjacent sides of the cardboard to increase its length and width by y units each. What will be the change in the area of the piece of cardboard? Show your work.

Part B: Bradley cut off rectangular strips from two adjacent sides of the cardboard to decrease its length and width by y units each. What will be the change in the area of the piece of cardboard? Show your work.

Answer 1

Part C: Bradley cut off a strip from one side of the cardboard and pasted the strip on an adjacent side of the cardboard to increase its length by y units and decrease its width by y units. What will be the change in the area of the cardboard? Show your work.

Answer 2

1.So, the dimensions of the square are x and x
Then,the area of the square piece=x*x=x^2
a)New length =x+y
New breadth=x+y
New area=(x+y)(x+y)=(x+y)^2
=x^2+2xy+y^2 { as (a+b)=a^2+b^2+2ab}
Change in area=new area-old area
=x^2+2xy+y^2-x^2
=2xy+y^2
b)New length =x-y
new breadth=x-y
new area=(x-y)(x-y)=(x-y)^2 {as (a-b)^2=a^2+b^2-2ab}
=x^2-2xy+y^2
Change in area=new area-old area
=x^2-2xy+y^2-x^2
=y^2-2xy
c)New lenght=x+y
new breadth=x-y
new area=(x+y)(x-y) {as (a+b)(a-b)=a^2-b^2}
=x^2-y^2
change in area=x^2-y^2-x^2
=-y^2

2.Length of rectangle = (4*2+2x-1)
=8-1+2x
=7+2x
Width of the rectangle=3*3-x+4
=9+4-x
=13-x
a)area of the rectangle=l*b
=(7+2x)(13-x)
=7(13-x)+2x(13-x)
=91-7x+26x-2x^2
=91+19x-2x^2 unit^2
b)Yes, as (7+2x)(13-x)=(13-x)(7+2x)=91+19x-2x^2 ( you can do the calculations if you want to check it.)
c)The degree of polynomial is 2 as the highest power is 2 and thus it is a quadratic polynomial (based upon its degree).You can also classify it as trinomial based upon the number of terms it contains.
Hope this helps and u understand all the identities i have used here

Answer 3

i do thanks!

Answer 4

wow thats a long problem

Answer 5

yes it is.