Question

Subtract the sum of (2m + 4n - 3p2) and (-m - n -p2) from the sum of(8m - 7n + 6p2) and (- 3m - 4n - p2) is
1) – 4m – 14n – 9p²
2) 4m - 14n + 9p2
3) - 4m + 14n + 9p2
4) – 4m + 14n - 9P²​

Answer 1

Answer:

The answer is (4m - 14n + 9p²). [Option 2]

Step-by-step explanation:

★ Sum of (2m + 4n - 3p²) and (-m - n -p²)

$\rm{=(2m + 4n - {3p}^{2} ) + (-m - n - {p}^{2})} \\ \rm{= \: 2m - m + 4n - n - {3p}^{2} - {p}^{2}} \: \\ \rm{= \: \green{m + 3n - 4 {p}^{2}}}$

$\rule{300}{1.5}$

★ Sum of (8m - 7n + 6p²) and (- 3m - 4n - p²)

$\rm{= \:(8m - 7n + 6 {p}^{2}) + (- 3m - 4n - {p}^{2} )} \\ \rm{= \:8m - 3m - 7n - 4n + 6 {p}^{2} - {p}^{2}} \\ \rm{= \:\blue{5m - 11n + 5 {p}^{2}}}$

$\rule{300}{1.5}$

★ Difference between (5m - 11n + 5p²) and (m + 3n - 4p²)

$\rm{= \: (5m - 11n + 5 {p}^{2} ) - (m + 3n - 4 {p}^{2} )} \\ \rm{= \:Change \: the \: Signs} \\ \rm{= \:(5m - 11n + 5 {p}^{2} ) - m - 3n + 4 {p}^{2}} \\ \rm{= \:5m - m - 11n - 3n + 5 {p}^{2} + 4 {p}^{2}} \\ \rm{= \:\pink{4m - 14n + 9 {p}^{2}}}$

$\therefore$ The answer is (4m - 14n + 9p²). [Option 2]

Answer 2

$\LARGE{\mathfrak{\underline{\underline{\red{Answer :-}}}}}$

✯ Case 1

Sum of (2m + 4n - 3p²) and (- m - n - p²)

${ \bf(2m \: + \: 4n \: - \: 3 {p}^{2}) + ( \: - \: m \: - \: n \: - \: {p}^{2} }$

$\mathrm{\gray{\bf{By \: removing \: brackets}}}$

$\bf{2m \: - \: m \: + \: 4n \: -n \: - \: {3p}^{2} \: - \: {p}^{2}}$

$\bf{\purple{ m \: + \: 3n \: - 4 {p}^{2}}}$

$\rule{200}{2}$

✯ Case 2

Sum of (8m - 7n + 6p²) and (-3m - 4n -p²)

$\bf{8m \: - \: 7n \: + \: 6 {p}^{2} } \\ \\ \bf{ \mathrm { \gray{By \: removing \: brackets}}} \\ \\ \bf {8m \: - 3m \: - \: 7n - 4n \: + 6 {p}^{2} } \\ \\ {\purple{\bf{5m \: - 11n \: + 5 {p}^{2} }}}$

$\rule{200}{2}$

✯ Case 3

Difference between (5m - 11 + 5p²) and (m + 3n - 4p²)

$\bf{(5m \: - \: 11 \: + \: 5 {p}^{2}) } \: \: - \: \: (m \: + \: 3n \: - \: 4 {p}^{2})$

We know that when there is negative( - ) sign before bracket then the sign inside the bracket got changed.

$\mathrm{\gray{\bf{By \: removing \: brackets}}}$

$\bf{ 5m \: - \: m \: - \: 11n \: - \: 3n \: + \: 5 {p}^{2} \: + \: 4 {p}^{2} } \\ \\ \bf{ \purple{4m \: - \: 14m \: + \: 9 {p}^{2} }}$

$\rule{200}{2}$

Option (b) is correct

$\huge{\pink{\underline{\boxed{\boxed{\red{\bf{ 4m \: - \: 14m \: + \: 9 {p}^{2} }}}}}}}$

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