Write the following cubes in expanded form (i) (2x+1)^3 , (ii) (2a -3b)^3 , (iii) (3/2x +1 )^3, (iv) (x- 2/3y)^3
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Answered by
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(i) (2x + 1)³
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Here,
x = 2x , y = 1
= (2x)³ + (1)³ + 3(2x)(1) {2x + 1}
= 8x³ + 1 + 6x {2x + 1}
= 8x³ + 1 + 6x(2x) + 6x(1)
= 8x³ + 1 + 12x² + 6x
= 8x³ + 12x² + 6x + 1
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(ii) (2a - 3b)³
[
Here,
x = 2a , y = 3b
= (2a)³ - (3b)³ - 3(2a)(3b) {2a - 3b}
= 8a³ - 27b³ - 18ab {2a - 3b}
= 8a³ - 27b³ - 18ab(2a) + 18ab(3b)
= 8a³ - 27b³ - 36a²b + 54ab²
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(iii) (
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Here,
x =
= (
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(iv) (x -
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Here,
x = x , y =
= (x)³ - (
= x³ -
= x³ -
= x³ -
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Answered by
50
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Q:-Write the following cubes in expanded form.
1)(2x+1)³
Using the formula ,
(x+y)³
=x³+3xy(x+y)+y³
★(2x)³+3(2x)(1){2x+1}+(1)³
=8x³+6x{2x+1}+1
=8x³+12x²+6x+1
2)(2a-3b)³
Using the formula
(x- y)³
=x³-3xy(x-y)-y³
★(2a)³-3(2a)(3b){2a-3b}
=8a³-18{2a-3b}-27b³
=8a³-27b³-36a²b+54ab²
3)(3/2x+1)³
Using the formula ,
(x+y)³
=x³+3xy(x+y)+y³
★(3/2x)³+3(3/2x)(1){3/2x+1)
=27/8x³+9/2x(3/2x+1)+1
=27/8x³+9/2x(3/2x)+9/2(1)
=27/8x³+27/4x²+9/2x+1
4)(x-2/3y)³
Using the formula
(x- y)³
=x³-3xy(x-y)-y³
★(x)³-3(x)(2/3y){x-2/3y}-(2/3y)³
=x³-2xy(x-2/3y)-8/27y³
=x³-2xy (x)+2xy(2/3y)-8/27y³
=x³-2x²y+4/3xy²-8/27y³
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