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Operations on Algebraic Expressions

Question

What must be added to $$ 2a^{3} + 5a - a^{2} - 6 $$ to get $$ a^{2} - a - a^{3} + 1 $$?

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Solution

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The answer can be obtained by subtracting from $$ 2a^{3} + 5a - a^{2} - 6 $$ to get $$ a^{2} - a - a^{3} + 1 $$
$$ = \left ( -a^{3} + a +1 \right ) - \left ( 2a^{3} + 5a - a^{2} - 6 \right ) $$
It can be written as
$$ -a^{3} + a^{2} - a + 1- 2a^{3} - 5a +a^{2} + 6 $$
By further calculation
$$-a^{3} + 2a^{2} - 6a + 7 $$

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Similar Questions

Q1

What must be added to $$ 2a^{3} + 5a - a^{2} - 6 $$ to get $$ a^{2} - a - a^{3} + 1 $$?

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Q2

What must be subtracted from a³ − 4a² + 5a − 6 to obtain a² − 2a + 1?

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Q3

What must be subtracted from a³ − 4a² + 5a − 6 to obtain a² − 2a + 1?

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Q4

(a) What should be added to

2 x^{2} + 6 x - 5

to get

3 x^{2} - 2 x + 6

?
(b) What must be subtracted from

a^{2} + b^{2} + c^{2} - 3 a b c

to get

2 a^{2} - b^{2} - 3 c^{2} + a b c

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Q5

If

a_{1} (> 0), a_{2}, a_{3}, a_{4}, a_{5}

are in a G.P.,

a_{2} + a_{4} =

2 a_{3} + 1 and 3 a_{2} + a_{3} = 2 a_{4},

then

a_{2} + a_{4} + 2 a_{5}

is equal to

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