Question

14. Fill in the blanks:
(i). (2x - 3y)^3 =
(ii). (2x + y - z)^2 = ...........
(iii). (3a + b)^3 = ....​

Answer 1

Step-by-step explanation:

[ 1 ]

${(2x - 3y)}^{3}$

_______

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

$=8x^3 - 36x^2y+54xy^2-27y^3$

$= 8 {x}^{3} - 18xy(2x - 3y) - 27 {y}^{3}$

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[ 2 ]

${(2x + y - z)}^{2}$

_________

$= (2x + y + {( - z))}^{2}$

$= {(2x)}^{2} + {y}^{2} + {( - z)}^{2} + 2(2x)(y) + 2(y)( - z) + 2( - z)(2x)$

$= 4 {x}^{2} + {y}^{2} + {z}^{2} + 4xy - 2yz - 4zx$

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[ 3 ]

${(3a + b)}^{3}$

_______

$= {(3a)}^{3} + {</strong><strong>3</strong><strong>(3a)}^{2} (b) + 3(3a) {(b)}^{2} + {(b)}^{3}$

$= 27 {a}^{3} + 27 {a}^{2} b + 9a {b}^{2} + {b}^{3}$

$= 27 {a}^{3} + 9ab(3a + b) + {b}^{3}$

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IDENTITIES USED

⚫( a -b )³= a³ - 3a²b + 3ab² - b³

⚫(a + b + c)² = a² + b²+ c²+ 2ab + 2bc + 2ca

⚫( a +b )³= a³ + 3 a²b + 3ab² + b³

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