A rectangle has a perimeter represented by the expression 6a−2.

Which expression represents the sum of the length and width of the rectangle?
−2
6a
3a−2
3a−1

The expression that represents the sum of the length and width of the rectangle is

Step-by-step explanation:

Given:

Perimeter of the rectangle  =  

To Find:

The sum of the length and width of the rectangle = ?

Solution:

We know that the perimeter of the rectangle is

=

=

From the given that we know

The sum of the length and  width is

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hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)