Answer to Question #212239 in Algebra for Tina

Question

Task

a) Evaluate each of the following expressions: 

i. 3(4−3)2 

ii. 3(5−3)2 

iii. 3(8−3)2

 iv. 3(10−3)2

b) In the expressions above, what parts are always the same? What part changes?

c) We can write an expression to represent all of the expressions in a) above if we use a letter for the part that changes. Write an expression using the letter x that could represent all of the numeric expressions in a).

d) What value of x would make your expression evaluate to 507? 

Answer 1

a)

i.

$$3(4-3)^2=3$$

ii.

$$3(5-3)^2=12$$

iii.

$$3(8-3)^2=75$$

iv.

$$3(10-3)^2=147$$

b) In the expressions above the first multiplier $3$ is the same, but the second multiplier changes from expression to expression.

In subtraction  the subtrahend $3$ is the same, but the minuend changes from expression to expression.

c)

$$3(x-3)^2$$

d)

$$3(x-3)^2=507$$

$$(x-3)^2=169$$

$$x-3=-\sqrt{169}\ \ or \ \ x-3=\sqrt{69}$$

$$x=3-13\ \ or \ \ x=3+13$$

$$x=-10\ \ or \ \ x=16$$