Simplify using following identity : (i) (2x + 3y)(4x^2 - 6xy + 9y^2) (ii) (3x - 5/x)(9x^2 + 15 + 25/x^2) (iii) (a/3 - 3b)(a^2/9 + ab + 9b^2)

(i) Given, ⇒ (2x + 3y)(4x 2 - 6xy + 9y 2 ) ⇒ (2x + 3y)[(2x) 2 - 2x × 3y + (3y) 2 ] Comparing above equation with , we get : a = 2x and b = 3y a 3 + b 3 = (2x) 3 + (3y) 3 = 8x 3 + 27y 3 . Hence, (2x + 3y)(4x 2 - 6xy + 9y 2 ) = 8x 3 + 27y 3 . (ii) Given, Comparing above equation with , we get : a = 3x and b = Hence, .

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

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If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

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If a + b = 11 and a² + b² = 65; find a³ + b³.

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If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.

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Mathematics

Simplify using following identity : (i) (2x + 3y)(4x^2 - 6xy + 9y^2) (ii) (3x - 5/x)(9x^2 + 15 + 25/x^2) (iii) (a/3 - 3b)(a^2/9 + ab + 9b^2)

Expansions

Related Questions

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

If a + b = 11 and a² + b² = 65; find a³ + b³.

If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.

Mathematics

Simplify using following identity : (i) (2x + 3y)(4x^2 - 6xy + 9y^2) (ii) (3x - 5/x)(9x^2 + 15 + 25/x^2) (iii) (a/3 - 3b)(a^2/9 + ab + 9b^2)

Expansions

Related Questions

If a - 2b + 3c = 0; state the value of a3 - 8b3 + 27c3.

If x + 5y = 10; find the value of x3 + 125y3 + 150xy - 1000.

If a + b = 11 and a2 + b2 = 65; find a3 + b3.

If x, y and z are three different numbers, then prove that :x2 + y2 + z2 - xy - yz - zx is always positive.

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

If a + b = 11 and a² + b² = 65; find a³ + b³.

If x, y and z are three different numbers, then prove that :
x² + y² + z² - xy - yz - zx is always positive.