Question 6 (b)

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

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Solution

While adding or subtracting algebraic expressions we need to be aware that we can add/subtract only like terms.
Like terms have the same algebraic factors.
According to question,
$⌊ (4 + 3 x) + (5 - 4 x + 2 x^{2}) ⌋ - ⌊ (3 x^{2} - 5 x) + (- x^{2} + 2 x + 5) ⌋$
$= [4 + 3 x + 5 - 4 x + 2 x^{2}] - [3 x^{2} - 5 x - x^{2} + 2 x + 5]$
$= [2 x^{2} + 3 x - 4 x + 5 + 4] - [3 x^{2} - x^{2} + 2 x - 5 x + 5]$
$= [2 x^{2} - x + 9] - [2 x^{2} - 3 x + 5]$
$= 2 x^{2} - x + 9 - 2 x^{2} + 3 x - 5$
$= 2 x^{2} - 2 x^{2} - x + 3 x + 9 - 5$
$= 2 x + 4$
So, the required expression is $2 x + 4$ .

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Similar questions

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

4 + 3 x a n d 5 - 4 x + 2 x^{2}

3 x^{2} - 5 x a n d - x^{2} + 2 x + 5

4 + 3 x

5 - 4 x + 2 x^{2}

3 x^{2} - 5 x

- x^{2} + 2 x + 5

4 + 3 x a n d 5 - 4 x + 2 x^{2}

3 x^{2} - 5 x a n d - x^{2} + 2 x + 5

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