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Maths-

General

Easy

Question

Which expression is equivalent to $left parenthesis 2 x to the power of 2 end exponent plus blank 3 x minus 2 right parenthesis minus left parenthesis 5 x to the power of 2 end exponent minus x minus 7 right parenthesis$ ?

$7 x^{2} + 4 x + 9$
$3 x^{2} + 4 x + 5$
$- 3 x^{2} + 2 x - 9$
$- 3 x^{2} + 4 x + 5$

The correct answer is: $negative 3 x to the power of 2 end exponent plus 4 x plus 5$

HINT: Use distributive law and simplify.
Complete step by step Solution
Distribute negative sign to each term in ( $5 x to the power of 2 end exponent minus x minus 7$ )
We get, $negative 5 x to the power of 2 end exponent plus x plus 7$
Hence the given expression becomes $2 x to the power of 2 end exponent plus blank 3 x minus 2 minus 5 x to the power of 2 end exponent plus x plus 7$
On adding the like terms of the simplified expression, we get
$2 x to the power of 2 end exponent plus blank 3 x minus 2 blank minus 5 x to the power of 2 end exponent plus x plus 7 equals blank minus 3 x to the power of 2 end exponent plus 4 x plus 5$
Thus, option D is the answer.
Note: We can also solve this question by subtraction that is:
$left parenthesis 2 x to the power of 2 end exponent plus blank 3 x minus 2 right parenthesis minus left parenthesis 5 x to the power of 2 end exponent minus x minus 7 right parenthesis equals blank minus 3 x to the power of 2 end exponent plus 4 x plus 5$
Thus, we get the correct answer.

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