Question

subtract the sum of (7m²+3n²+6p²)and(3m²-5n²+6p²) from the sum of (2m²-6n²+11p²) and (-6m²+6n²-6p²)​

Answer 1

$firstly \: find \: the \: sum \: of \: (7m²+3n²+6p²)and(3m²-5n²+6p²)$

$(7m²+3n²+6p²)and(3m²-5n²+6p²) \\ \\ (7m²+3n²+6p²) + (3m²-5n²+6p²) \\ (7m²+3n²+6p² + 3m²-5n²+6p²) \\ 7m {}^{2} + 3m {}^{2} + 3n {}^{2} - 5n {}^{2} + 6p {}^{2} + 6p {}^{2} \\ 10m {}^{2} - 2n {}^{2} + 12p {}^{2}$

THE SUM OF (7m²+3n²+6p²)and(3m²-5n²+6p²) is 10m²-2n²+12p²

Now, find the sum of (2m²-6n²+11p²) and (-6m²+6n²-6p²)

$(2m²-6n²+11p²) and (-6m²+6n²-6p²) \\ (2m²-6n²+11p²) + (-6m²+6n²-6p²) \\ 2m²-6n²+11p²-6m²+6n²-6p²\\ 2m^{2} - 6m {}^{2} - 6n {}^{2} + 6n {}^{2} + 11p {}^{2} - 6p {}^{2} \\ - 4m {}^{2} + 5p {}^{2}$

THE SUM OF (2m²-6n²+11p²) and (-6m²+6n²-6p²) IS -4m²+5p²

NOW SUBTRACT THE SUM

$(10m²-2n²+12p²) - (4m²+5p²) \\ 10m {}^{2} - 2n {}^{2} + 12p {}^{2} - 4m {} ^{2} - 5p {}^{2} \\ 10m {}^{2} - 4m {}^{2} - 2n {}^{2} + 12p {}^{2} - 5p {}^{2} \\ 6m {}^{2} - 2n {}^{2} + 7p {}^{2}$

THANKU❤

Answer 2

firstly \: find \: the \: sum \: of \: (7m²+3n²+6p²)and(3m²-5n²+6p²)firstlyfindthesumof(7m²+3n²+6p²)and(3m²−5n²+6p²)

\begin{gathered}(7m²+3n²+6p²)and(3m²-5n²+6p²) \\ \\ (7m²+3n²+6p²) + (3m²-5n²+6p²) \\ (7m²+3n²+6p² + 3m²-5n²+6p²) \\ 7m {}^{2} + 3m {}^{2} + 3n {}^{2} - 5n {}^{2} + 6p {}^{2} + 6p {}^{2} \\ 10m {}^{2} - 2n {}^{2} + 12p {}^{2} \end{gathered}

(7m²+3n²+6p²)and(3m²−5n²+6p²)

(7m²+3n²+6p²)+(3m²−5n²+6p²)

(7m²+3n²+6p²+3m²−5n²+6p²)

7m

2

+3m

2

+3n

2

−5n

2

+6p

2

+6p

2

10m

2

−2n

2

+12p

2

THE SUM OF (7m²+3n²+6p²)and(3m²-5n²+6p²) is 10m²-2n²+12p²

Now, find the sum of (2m²-6n²+11p²) and (-6m²+6n²-6p²)

\begin{gathered}(2m²-6n²+11p²) and (-6m²+6n²-6p²) \\ (2m²-6n²+11p²) + (-6m²+6n²-6p²) \\ 2m²-6n²+11p²-6m²+6n²-6p²\\ 2m^{2} - 6m {}^{2} - 6n {}^{2} + 6n {}^{2} + 11p {}^{2} - 6p {}^{2} \\ - 4m {}^{2} + 5p {}^{2} \end{gathered}

(2m²−6n²+11p²)and(−6m²+6n²−6p²)

(2m²−6n²+11p²)+(−6m²+6n²−6p²)

2m²−6n²+11p²−6m²+6n²−6p²

2m

2

−6m

2

−6n

2

+6n

2

+11p

2

−6p

2

−4m

2

+5p

2

THE SUM OF (2m²-6n²+11p²) and (-6m²+6n²-6p²) IS -4m²+5p²

NOW SUBTRACT THE SUM

\begin{gathered}(10m²-2n²+12p²) - (4m²+5p²) \\ 10m {}^{2} - 2n {}^{2} + 12p {}^{2} - 4m {} ^{2} - 5p {}^{2} \\ 10m {}^{2} - 4m {}^{2} - 2n {}^{2} + 12p {}^{2} - 5p {}^{2} \\ 6m {}^{2} - 2n {}^{2} + 7p {}^{2} \end{gathered}

(10m²−2n²+12p²)−(4m²+5p²)

10m

2

−2n

2

+12p

2

−4m

2

−5p

2

10m

2

−4m

2

−2n

2

+12p

2

−5p

2

6m

2

−2n

2

+7p

2