Question

5 c.) (25m - n)^3+ (25m + n)3
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Answer 1

Step-by-step explanation:

$(25m - n)^3+ (25m + n)3 \\ = (25m - n+ 25m + n)[(25m - n)^2 - (25m - n)(25m + n) + (25m + n)² ] \\ = (50m)[(625 {m}^{2} + {n}^{2} - 50mn -( 25 {m}^{2} - {n}^{2} ) + 625 {m}^{2} + {n}^{2} + 50mn] \\ = 50m(1250 {m}^{2} + 2 {n}^{2} - 25 { {m}^{2} - {n}^{2} }) \\ = 50m(1225 {m}^{2} - {n}^{2} )$

Answer 2

given★

• $= (25 - n) {}^{3} + (25 + n) {}^{3}$

EVALUATION★

$(25m - n) {}^{3} + (25m + n) {}^{3}$

can be this written as

• $= (25m) {}^{3} - n {}^{3} - 3(25m) {}^{2}(n) + 3(25m)n {}^{2} + (25m) {}^{3} + n {}^{3} + 3(25m) {}^{2} (n) + 3(25m)(n) {}^{2}$
• $= 15625m^2 + 75n {}^{2} + 15625m^2 + 75mn {}^{2} \\ \\ = 31250m^2 + 150mn {}^{2}$
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formula uses★

$= > (a + b) {}^{3} = a {}^{3} + b {}^{3} + 3a {}^{2}b + 3ab {}^{2}$

$= > (a - b) {}^{3} = a {}^{3} - b {}^{3} - 3a {}^{2}b + 3ab {}^{2}$

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I hope it helps you