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Sequence

How much more...

Question

How much more than
$2 x^{2} + 4 x y + 2 y^{2} i s 5 x^{2} + 10 x y - y^{2}$

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Solution

Let $5 x^{2} + 10 x y - y^{2}$ is A more than $2 x^{2} + 4 x y + 2 y^{2}$

$∴ 5 x^{2} + 10 x y - y^{2}$ $= A + (2 x^{2} + 4 x y + 2 y^{2})$
$\Rightarrow A = (5 x^{2} + 10 x y - y^{2})$ $- (2 x^{2} + 4 x y + 2 y^{2})$
(Multiply the minus (−) sign inside the bracket)
$A$ $= 5 x^{2} + 10 x y - y^{2} - 2 x^{2} - 4 x y - 2 y^{2}$
$A = (5 x^{2} - 2 x^{2}) + (10 x y - 4 x y) + (- y^{2} - 2 y^{2})$
$A$ $(5 - 2) x^{2} + (10 - 2) x y + (- 1 - 2) y^{2}$
$A = 3 x^{2} + 6 x y - 3 y^{2}$

Hence, the expression $5 x^{2} + 10 x y = y^{2}) i s (3 x^{2} + 6 x y - 3 y^{2})$ more than $2 x^{2} + 4 x y + 2 y^{2}$ .

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Similar questions

(i) How much more than $2 x^{2} + 4 x y + 2 y^{2} i s 5 x^{2} + 10 x y - y^{2} ?$

(ii) How much less than $2 a^{2} + 1 i s t h a n 3 a^{2} - 6 ?$

Q. Subtract x²− 2xy + 5y² − 4 from 4xy − 5x² − y² + 6.

Write the coefficient of:

$(i) a b i n 7 a b x, (i i) 7 a i n 7 a b x; (i i i) 5 x^{2} i n 5 x^{2} - 5 x; (i v) 8 i n a^{2} - 8 a x + a; (v) 4 x y i n x^{2} - 4 x y + y^{2} .$

Q. What should be added to 5x² + 2xy + y² to get 3x² + 4xy?

Q. How much more than

2 x^{2} + 4 x y + 2 y^{2}

5 x^{2} + 10 x y - y^{2}

?
State True or False: The answer is

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

.

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