From the sum of $4 + 3 x$ and $5 - 4 x + 2 x^{2}$ , subtract the sum of $3 x^{2} - 5 x$ and $- x^{2} + 2 x + 5$ .

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Solution

Express the given statement as an algebraic expression and simplify :
Given expressions are:
$4 + 3 x$
$5 - 4 x + 2 x^{2}$
$3 x^{2} - 5 x$
$- x^{2} + 2 x + 5$
Firstly, find sum of $4 + 3 x$ and $5 - 4 x + 2 x^{2}$
$(4 + 3 x) + (5 - 4 x + 2 x^{2}) = 2 x^{2} - x + 9$ $. . . (1)$
Then, find sum of $3 x^{2} - 5 x$ and $- x^{2} + 2 x + 5$
$(3 x^{2} - 5 x) + (- x^{2} + 2 x + 5) = 2 x^{2} - 3 x + 5$ $. . . (2)$
Finally, Subtract $(2)$ from $(1)$
$∴ (2 x^{2} - x + 9) - (2 x^{2} - 3 x + 5) = 2 x + 4$
Hence, the result is $2 x + 4$

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From the sum of $4 + 3 x$ and $5 - 4 x + 2 x^{2}$ , subtract the sum of $3 x^{2} - 5 x$ and $- x^{2} + 2 x + 5$ .

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