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. (4 points)

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

@perl @satellite73 @shrutipande9 @dan815

Answer 3

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.Thank U.

Answer 4

The area of each original square is : A = x^2 ........... A = s^2........... s= side of the square

A) L = x + y and W= x + y

Area = ( x + y )^2 = x^2 + 2xy + y^2

Increase in area : Ad= x^2 + 2xy + y^2 - x^2 = 2xy + y^2

B ) The figure is a square of side ( x - y ) its area is A = ( x - y )^2 = x^2 - 2xy + y^2

The change in area is : Ad = x^2 - 2xy + y^2 - x^2 = y^2 - 2xy

c) The rectangle is L = x + y and W= x - y

The area of the rectangle is A = L x W

Then the area is A = ( x + y )( x - y ) = x^2 - y^2

The new area is; x^2 - y^2 - x^2 = - y^2 .......... Negative means a decrease

The new area decreases by y^2

2)

A) The area is A= L x W

... A = ( 4x^2 + 2x - 1 )( 3x^3 -x + 4 ) = 12x^5 - 4x^3 + 16x^2 + 6x^4 -2x^2 + 8x - 3x^3 +x - 4

... A = 12x^5 + 6x^4 -7x^3 + 14x^2 + 9x - 4........... AREA

B) Yes, polynomials are closed over multiplication because the product of two polynomials is a polynomial.

C) It is a polynomial of 5th degree in one variable.

Answer 5

i dont undeerstand your expplantion

Answer 6

@perl

Answer 7

lets start with a drawing