Factor completely x3y6 – 64

x 3 y 6 − 64

is the difference of two cubes and can be factored in the following pattern.

a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 )

a 3

factors to a

b 3

factors to b

The pattern of the signs follows the acronym SOAP

S = same sign as the cubes

O = opposite sins of the cubes

AP = always positive

x 3 y 3

factors to xy

64

factors to 4

x 3 y 3 − 64 = ( x y − 4 ) ( x 2 y 2 + 4 x y + 16 )

Step-by-step explanation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl