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(a-b)^2 Expansion and Visualisation

From the sum ...

Question

From the sum of

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

subtract the sum of

$3 x^{2} - 5 x a n d - x^{2} + 2 x + 5$ . [4 MARKS]

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Solution

Forming the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

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

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^{3} - 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

(4 + 3 x - x^{2})

(5 - 4 x + 2 x^{2})

(3 x^{2} - 5 x)

(- x^{2} + 2 x + 5)

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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