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Question

Which of the following is an equivalent form of the expression?
$left parenthesis 2 x minus 2 right parenthesis squared minus left parenthesis 2 x minus 2 right parenthesis$

$2 x^{2} - 6 x + 6$
$4 x^{2} - 10 x + 2$
$(2 x - 2) (2 x - 2)$
$(2 x - 3) (2 x - 2)$

hint Hint:

Hint:
The distributive law of multiplication over addition says
$a times left parenthesis b plus c right parenthesis equals a times b plus a times c$
We are given an expression which has two terms. First, we need to check if we can take some linear factor common from these two terms. Then we use the distributive law and further we need to simplify the rest of the expression in the brackets. If there are no factors to take common, then we simplify the expression directly.

The correct answer is: $left parenthesis 2 x minus 3 right parenthesis left parenthesis 2 x minus 2 right parenthesis$

The given expression is
$left parenthesis 2 x minus 2 right parenthesis squared minus left parenthesis 2 x minus 2 right parenthesis$
We can see that the first term has the factor $left parenthesis 2 x minus 2 right parenthesis$ twice and the second term is $left parenthesis 2 x minus 2 right parenthesis$
So we can take this factor common. Comparing with the distributive law , we get $a equals 2 x minus 2 comma b equals 2 x minus 2 comma c equals negative 1$
Putting these values in the distributive law, we get
$left parenthesis 2 x minus 2 right parenthesis squared minus left parenthesis 2 x minus 2 right parenthesis equals left parenthesis 2 x minus 2 right parenthesis left curly bracket left parenthesis 2 x minus 2 right parenthesis minus 1 right curly bracket$
Simplifying, we get
$left parenthesis 2 x minus 2 right parenthesis squared minus left parenthesis 2 x minus 2 right parenthesis equals left parenthesis 2 x minus 2 right parenthesis left parenthesis 2 x minus 3 right parenthesis$
Thus, the correct option is D) $left parenthesis 2 x minus 2 right parenthesis left parenthesis 2 x minus 3 right parenthesis$

Note:
Another way to solve this problem is to expand or simplify the expression given in the question. Then we expand the expressions given in the options and check which one of them is equal to the one given in question.
We need to be careful while simplifying the expressions

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Which of the following is an equivalent form of the expression?

The correct answer is:

The given expression isWe can see that the first term has the factor twice and the second term is So we can take this factor common. Comparing with the distributive law , we get Putting these values in the distributive law, we getSimplifying, we getThus, the correct option is D)

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Which of the following is an equivalent form of the expression?
$left parenthesis 2 x minus 2 right parenthesis squared minus left parenthesis 2 x minus 2 right parenthesis$

The correct answer is: $left parenthesis 2 x minus 3 right parenthesis left parenthesis 2 x minus 2 right parenthesis$

Write a congruence statement for the triangles. Identify all pairs of congruent corresponding
parts.

Write a congruence statement for the triangles. Identify all pairs of congruent corresponding
parts.

Each co-ordinate (x, y) of the blue figure gets translated horizontally _ units and vertically _ units.

Each co-ordinate (x, y) of the blue figure gets translated horizontally _ units and vertically _ units.