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Addition and Subtraction of Algebraic Expression

Subtract 2x...

Question

Subtract $2 x^{3} - x^{2} + 4 x - 6$ from $x^{3} + 5 x^{2} - 4 x + 6$ .

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Solution

$(x^{3} + 5 x^{2} - 4 x + 6) - (2 x^{3} - x^{2} + 4 x - 6)$
$= x^{3} + 5 x^{2} - 4 x + 6 - 2 x^{3} + x^{2} - 4 x + 6$
$= (1 - 2) x^{3} + (5 + 1) x^{2} + (- 4 - 4) x + (6 + 6)$
$= - 1 x^{3} + 6 x^{2} - 8 x + 12$
$= - x^{3} + 6 x^{2} - 8 x + 12$

Hence, $(x^3 + 5x^2 -4x + 6)- (2x^3 -x^2 + 4x -6)=- x^3 + 6x^2 -8x + 12$.

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Similar questions

Q. State True or False:
On subtracting

x^{3} - 4 x - 1

3 x^{3} - x^{2} + 6

, the answer is

2 x^{3} - x^{2} + 4 x + 7

.

Q. must be subtracted from

(x^{3} - 3 x^{2} + 5 x - 1)

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

Q. Match the following.

	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

Q. What must be subtracted from (x⁴+ 2x³– 2x² + 4x + 6) so that the result is exactly divisible by (x²+ 2x – 3)?

$- x^{3} - 4 x^{2} + 9 x - 3$ must be subtracted from $x^{3} - 3 x^{2} + 5 x - 1$ to get $2 x^{3} + x^{2} - 4 x + 2$ . State true or false.

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