Question

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Answer 1

Step-by-step explanation:

$\bf{\undetline{\underline\red{To\:Find:-}}}$

• (i) 2x² + 3y² - 5xy + 5x² - y² + 6xy - 3x²

• (ii) 3xy² - 5x²y + 7xy - 8xy² - 4xy + 6x²y

• (iii) 5x⁴ - 7x² + 8x - 1 + 3x³- 9x² + 7 - 3x⁴ + 11x - 2 + 8x².

$\bf{\undetline{\underline\green{Solution:-}}}$

(i) 2x² + 3y² - 5xy + 5x² - y² + 6xy - 3x²

= 2x² + 5x² - 3x² + 3y² - y² - 5xy + 6xy

= 7x² - 3x² + 3y² - y² + xy

= 4x² + 2y² + xy

= 4x² + xy + 2y²

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(ii) 3xy² - 5x²y + 7xy - 8xy² - 4xy + 6x²y

= 3xy² - 8xy² - 5x²y + 6x²y + 7xy - 4xy

= - 5xy² + x²y + 3xy

= x²y + 3xy - 5xy²

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(iii) 5x⁴ - 7x² + 8x - 1 + 3x³- 9x² + 7 - 3x⁴ + 11x - 2+ 8x².

=5x⁴ -3x⁴ + 3x³ -7x² - 9x² + 8x² + 8x + 11x - 1 - 2 + 7

= 2x⁴ + 3x³ - 16x² + 8x² + 19x + 7 -3

= 2x⁴ + 3x³ - 8x² + 19x + 4

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Required answers:-

• (i) 4x² + xy + 2y²

• (i) 4x² + xy + 2y²(ii) x²y + 3xy - 5xy²

• (i) 4x² + xy + 2y²(ii) x²y + 3xy - 5xy²(iii) 2x⁴ + 3x³ - 8x² + 19x + 4

Answer 2

$\huge\rm {Question}$

$\bf\red {2 {x}^{2} + 3 {y}^{2} - 5xy + 5 {x}^{2} - {y}^{2} + 6xy - 3 {x}^{2}}$

$\huge\rm {Solution }$

$\sf {\implies {2x}^{2} + 5 {x}^{2} - {3x}^{2} + 3 {y}^{2} - {y}^{2} - 5xy + 6xy}$

[ Collecting all like terms]

$\sf {\implies 7 {x}^{2} - 3 {x}^{2} + 2 {y}^{2} + xy}$

[ Performing addition and subtraction of like terms]

$\sf\green {\implies 4 {x}^{2} + 2 {y}^{2} + xy \: ans..}$

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$\huge\rm {Question}$

$\bf\red {3x {y}^{2} - 5 {x}^{2} y + 7xy - 8x {y}^{2} - 4xy + 6 {x}^{2} y}$

$\huge\rm {Solution}$

$\sf {\implies 3x {y}^{2} - 8x {y}^{2} - 5 {x}^{2} y + 6 {x}^{2} y + 7xy - 4xy}$

[ Collecting all like terms]

$\sf\green {\implies - 5x {y}^{2} + {x}^{2} y + 3xy \: ans...}$

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$\huge\rm {Question}$

$\bf\red {5 {x}^{4} - 7 {x}^{2} + 8x - 1 + 3 {x}^{3} - 9 {x}^{2} + 7 - 3 {x}^{2} + 11x - 2 + 8 {x}^{2}}$

$\huge\rm {Solution }$

$\sf { \implies 5 {x}^{4} - {3x}^{4} - 7 {x}^{2} - 9 {x}^{2} + 8 {x}^{2} + 8x + 11x - 1 + 7 - 2 + 3 {x}^{3}}$

[ Collecting all like terms]

$\sf {\implies 2 {x}^{4} - 16 {x}^{2} + 8 {x}^{2} + 19x + 6 - 2 + 3 {x}^{3}}$

[ Performing addition and subtraction]

$\sf { \implies 2 {x}^{4} - 8 {x}^{2} + 19x + 4 + 3 {x}^{3}}$

$\sf\green { \implies {2x}^{4} + 3 {x}^{3} - 8 {x}^{2} + 19x + 4 \: ans...}$

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