Question

1. Multiply (5x - y)(3x^2 + 4xy + y^2), and verify the result by taking x=-2 and y = 2.
2. Find the product of the algebraic expressions (2x^2- 5x + 1) and (7x^3 - 5x^2 + 3x + 2).

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Answer 1

• Preview the attached picture for solution of 1st Question. {sorry for bad handwriting]

2.

$\to \bf( {2x}^{2} - 5x + 1)( {7x}^{3} - {5x}^{2} + 3x + 2 )$

$\small \sf \to{2x}^{2} ({7x}^{3} - {5x}^{2} + 3x + 2) - 5x({7x}^{3} - {5x}^{2} + 3x + 2) + 1({7x}^{3} - {5x}^{2} + 3x + 2)$

$\small \sf \to{{14x}^{5} - {10x}^{4} + {6x}^{3} + {4x}^{2} - {35x}^{4} + {25x}^{3} - {15x}^{2} - 10x + {7x}^{3} - {5x}^{2} + 3x + 2}$

• Rearranging like terms,

$\small \sf \to{14x}^{5} - {10x}^{4} - {35x}^{4} + {6x}^{3} + {25x}^{3} + {7x}^{3}+ {4x}^{2} - {5x}^{2} - {15x}^{2} - 10x + 3x + 2$

$\small \to \boxed{\sf \red{ {14x}^{5} }- \red{ {45x}^{4} } + \red{{38x}^{3} } - \red{{16x}^{2} } - \red{7x }+ \red{2}}$

Answer 2

Preview the attached picture for solution of 1st Question. {sorry for bad handwriting]

2.

Rearranging like terms,