Prove algebraically that (m + 2)2 – m 2 – 12 is always a multiple of 4

Step-by-step explanation:

Step 1:

Write the expression

Step 2: Expand

Step 3: Collect similar terms

Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.

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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is