| (a) What should be added to \[{{x}^{2}}+xy+{{y}^{2}}\]to obtain \[2{{x}^{2}}+\text{ }3xy?\] |
| (b) What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16? |
Answer:
(a) Required expression is equal to the subtraction of\[{{x}^{2}}+xy+{{y}^{2}}\text{ }from\,\,2{{x}^{2}}+3xy\].
Hence, required expression
\[=\left( 2{{x}^{2}}+3xy \right)\left( {{x}^{2}}+xy+{{y}^{2}} \right)\]
\[=2{{x}^{2}}+3xy{{x}^{2}}xy{{y}^{2}}\]
\[=2{{x}^{2}}{{x}^{2}}+3xyxyy2\]
\[=\left( 21 \right){{x}^{2}}+\left( 31 \right)xy{{y}^{2}}\]
\[={{x}^{2}}+2xy{{y}^{2}}\]
(b) Let P denote the required expression, then
(2a + 8b + 10) ? P = ? 3a + 7b + 16
Hence, required expression P
= (2a + 8b + 10) ? (? 3a + 7b + 16)
= 2a + 8b + 10 + 3a ? 7b ? 16
= 2a + 3a + 8b ? 7b + 10 ? 16
= (2 + 3) a + (8 ? 7) b + (10 ? 16)
= 5a + b ? 6
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