Question

Subtract the sum of 3y^2 -z^ 2 and – y ^2 + yz +z^2 from the sum of 4y^2 –z 2 and –y 2 +yz + 6z2

Answer 1

$\large\sf\underline{Question:}$

Subtract the sum of $\sf\:3y^{2} -z^{2}$ and $\sf\:– y^{2} + yz +z^{2}$ from the sum of $\sf\:4y^{2} –z^{2}$ and $\sf\:–y^{2} +yz + 6z^{2}$

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$\large\sf\underline{Answer:}$

$\small\rm\red\star\:\underline{First\:Step-}$

Let's find :

Sum of $\sf\:3y^{2} -z^{2}$ and $\sf\:- y^{2} + yz +z^{2}$

$\sf➻\:3y^{2} -z^{2}+(- y^{2} + yz +z^{2})$

$\sf➻\:3y^{2} -z^{2} - y^{2} + yz +z^{2}$

$\sf➻\:3y^{2} - y^{2} - z^{2} +z^{2} + yz$

$\sf➻\:2y^{2} - \cancel{z^{2}}+\cancel{z^{2}} + yz$

${\sf{{\purple{➞\:2y^{2}+yz}}}}$

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$\small\rm\red\star\:\underline{Second\:Step-}$

Let's find :

Sum of $\sf\:4y^{2} –z^{2}$ and $\sf\:–y^{2} +yz + 6z^{2}$

$\sf➻\:4y^{2} -z^{2}+(- y^{2} + yz +6z^{2})$

$\sf➻\:4y^{2} -z^{2} - y^{2} + yz +6z^{2}$

$\sf➻\:4y^{2} - y^{2} - z^{2} +6z^{2} + yz$

$\sf➻\:3y^{2} - z^{2} + 6z^{2} + yz$

${\sf{{\purple{➞\:3y^{2}+ 5z^{2} +yz}}}}$

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$\small\rm\red\star\:\underline{Final\:Step-}$

Let's subtract :

$\sf\:2y^{2}+yz$ from $\sf\:3y^{2}+ 5z^{2} +yz$

$\sf➻\:3y^{2}+ 5z^{2} +yz - (2y^{2}+yz)$

$\sf➻\:3y^{2}+ 5z^{2} +yz - 2y^{2}- yz$

$\sf➻\:3y^{2}- 2y^{2}+ 5z^{2} +yz-yz$

$\sf➻\:y^{2}+ 5z^{2} +\cancel{yz}-\cancel{yz}$

${\sf{{\purple{➞\:y^{2}+5z^{2}}}}}$

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!! Hope it helps !!