Your answer is mathematically correct, but it's in vertex form.
Expand and simplify it to put it in factored form.
Write an expression in factored form for the area of the shaded portion of the figure. (In the figure, a = 3 and b = 5.)
The figure is in this website below:
www.webassign.net/laratrmrp6/p-3-162-alt.gif
The answer i got: (5(x+5)^2)/6 - 15/2. but online website (where i do my assignments that is posted by my teacher), says it is wrong, i just don't understand why.
3 answers
Area of big triangle A1 = 1 / 2 [ 5 / a ∙ ( x + b ) ]
Area of small triangle A2 = 1 / 2 ( 5 ∙ a )
Area of shaded portion = Area of big triangle - Area of small triangle
A = A1 - A2
A = 1 / 2 ( 5 / a ) ∙ ( x + b ) ( x + b ) - 1 / 2 ( 5 ∙ a ) =
1 / 2 [ 5 / a ∙ ( x + b )² - 5 a ] =
1 / 2 [ 5 / a ∙ ( x + b )² - 5 a² / a ] =
1 / 2a [ 5 ∙ ( x + b )² - 5 a² ] =
5 / 2a [ ( x + b )² - a² ) ] =
5 / 2a ( x + b + a ) ( x + b - a )
_____________________________
Remark:
m² - n² = ( m + n ) ( m - n)
so
( x + b )² - a² = ( x + b + a ) ( x + b - a )
_______________________________
Area of small triangle A2 = 1 / 2 ( 5 ∙ a )
Area of shaded portion = Area of big triangle - Area of small triangle
A = A1 - A2
A = 1 / 2 ( 5 / a ) ∙ ( x + b ) ( x + b ) - 1 / 2 ( 5 ∙ a ) =
1 / 2 [ 5 / a ∙ ( x + b )² - 5 a ] =
1 / 2 [ 5 / a ∙ ( x + b )² - 5 a² / a ] =
1 / 2a [ 5 ∙ ( x + b )² - 5 a² ] =
5 / 2a [ ( x + b )² - a² ) ] =
5 / 2a ( x + b + a ) ( x + b - a )
_____________________________
Remark:
m² - n² = ( m + n ) ( m - n)
so
( x + b )² - a² = ( x + b + a ) ( x + b - a )
_______________________________
Thanks Bosnian