Simplify-1 m-n3-m-n32 y-x3-y-x33 2-p3-2-p34 2 a-93-2 a-935 5 a-3 c3-5 a-3 c3

(1) (m + n)3 + (m minus; n)3 =m3+n3+3m2n+3mn2+m3 n3 3m2n+3mn2= #160;2m3+6mn2 (2) (y minus; x)3 minus; (y + x)3 =y3 x3 3y2x+3yx2 y3+x3+3y2x+3yx2=y3 x ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expression

Simplify:1 m+...

Question

Simplify:

(1) (m + n)³ + (m − n)³
(2) (y − x)³ − (y + x)³
(3) (2 − p)³ + (2 + p)³
(4) (2a − 9)³ − (2a + 9)³
(5) (5a + 3c)³ − (5a − 3c)³

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Solution

(1) (m + n)³ + (m − n)³
$= m^{3} + n^{3} + 3 m^{2} n + 3 m n^{2} + m^{3} - n^{3} - 3 m^{2} n + 3 m n^{2} = 2 m^{3} + 6 m n^{2}$

(2) (y − x)³ − (y + x)³
$= (y^{3} - x^{3} - 3 y^{2} x + 3 y x^{2}) - (y^{3} + x^{3} + 3 y^{2} x + 3 y x^{2}) = y^{3} - x^{3} - 3 y^{2} x + 3 y x^{2} - y^{3} - x^{3} - 3 y^{2} x - 3 y x^{2} = - 2 x^{3} - 6 x y^{2}$

(3) (2 − p)³ + (2 + p)³
$= 8 - p^{3} - 12 p + 6 p^{2} + 8 + p^{3} + 12 p + 6 p^{2} = 16 + 12 p^{2}$

(4) (2a − 9)³ − (2a + 9)³
$= (8 a^{3} - 729 - 108 a^{2} + 486 a) - (8 a^{3} + 729 + 108 a^{2} + 486 a) = 8 a^{3} - 729 - 108 a^{2} + 486 a - 8 a^{3} - 729 - 108 a^{2} - 486 a = - 216 a^{2} - 1458$

(5) (5a + 3c)³ − (5a − 3c)³
$= 125 a^{3} + 27 c^{3} + 225 a^{2} c + 135 a c^{2} - (125 a^{3} - 27 c^{3} - 225 a^{2} c + 135 a c^{2}) = 125 a^{3} + 27 c^{3} + 225 a^{2} c + 135 a c^{2} - 125 a^{3} + 27 c^{3} + 225 a^{2} c - 135 a c^{2} = 54 c^{3} + 450 a^{2} c$

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Simplify: (1) (m + n)3 + (m − n)3 (2) (y − x)3 − (y + x)3 (3) (2 − p)3 + (2 + p)3 (4) (2a − 9)3 − (2a + 9)3 (5) (5a + 3c)3 − (5a − 3c)3

Simplify:

(1) (m + n)³ + (m − n)³
(2) (y − x)³ − (y + x)³
(3) (2 − p)³ + (2 + p)³
(4) (2a − 9)³ − (2a + 9)³
(5) (5a + 3c)³ − (5a − 3c)³