Find he products of the following expression
(i) $(4 x + 3 y) (16 x^{2} - 12 x y + 9 y^{2})$
(ii) $(5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})$

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Solution

(i) $(4 x + 3 y) (16 x^{2} - 12 x y + 9 y^{2})$
$= (4 x + 3 y) [(4 x)^{2} - (4 x) \times (3 y) + (3 y)^{2}]$
$= (a + b) (a^{2} - a b + b^{2})$ [Where a = 4x, b = 3y]
$= a^{3} + b^{3} = (4 x)^{3} + (3 y)^{3} = 64 x^{3} + 27 y^{3}$
(ii) $(5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})$
$= (5 x - 2 y) [(5 x)^{2} + (5 x) \times (2 y) + (2 y)^{2}]$
$= (a - b) (a^{2} + a b + b^{2})$ [Where a = 5x, b = 2y]
$= a^{3} - b^{3} = (5 x)^{3} - (2 y)^{3} = 125 x^{3} - 8 y^{3}$

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Simplify :

7 x^{3} + 8 y^{3} - (4 x + 3 y) (16 x^{2} - 12 x y + 9 y^{2})

Q. The product of

(4 x - 3 y)

and

(16 x^{2} + 12 x y + 9 y^{2})

Find the following products:

(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

(iv) (3x − 4y + 5z) (9x² +16y²+ 25z² + 12xy −15zx + 20yz)

Q. Find the product of

2 x^{2} - 12 x y + 9 y^{2}

and

x + y

Q. Subtract the product of

(x + y) (5 x - y)

from the product of

(3 x + y) (x + 5 y)

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Find he products of the following expression(i) (4x+3y)(16x2−12xy+9y2)(ii) (5x−2y)(25x2+10xy+4y2)

(i) (4x+3y)(16x2−12xy+9y2)=(4x+3y)[(4x)2−(4x)×(3y)+(3y)2]=(a+b)(a2−ab+b2) [Where a = 4x, b = 3y]=a3+b3=(4x)3+(3y)3=64x3+27y3(ii) (5x−2y)(25x2+10xy+4y2)=(5x−2y)[(5x)2+(5x)×(2y)+(2y)2]=(a−b)(a2+ab+b2) [Where a = 5x, b = 2y]=a3−b3=(5x)3−(2y)3=125x3−8y3

Find he products of the following expression
(i) $(4 x + 3 y) (16 x^{2} - 12 x y + 9 y^{2})$
(ii) $(5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})$