Question

Realiza las siguientes operaciones entre monomios:
a) –x2 + x + x2 + x3 + x b) 8xy2 – 5x2y + x2y - xy2 c) 8x2 – x + 9x + x2
d) 2x2 ·4x3 ·5x6
e) –3x2 · xyz · 6y3 · x2 f)15x3 :5x2
g) –8x3y2 : 2x2y
h) 10x4yz2 : 5xyz

Answer 1

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

$b)8x {y}^{2} - 5 {x}^{2} y + {x}^{2} y - x {y}^{2} = \\ (8x{y}^{2} - x {y}^{2} ) + ( - 5 {x}^{2}y + {x}^{2} y ) = \\ 7x {y}^{2} + ( - 4 {x}^{2} y) = \\ 7x {y}^{2} - 4 {x}^{2} y = \\ xy(7y - 4x)$

$c)8 {x}^{2} - x + 9x + {x}^{2} = \\ (8 {x}^{2} + {x}^{2} ) + ( - x + 9x) = \\ 9 {x}^{2} + 8x = \\ x(9x + 8)$

$d)2 {x}^{2} \times 4 {x}^{3} \times 5 {x}^{6} = \\ 2 \times 4 \times 5 \times {x}^{2 + 3 + 6} = \\ 40 {x}^{11}$

$e) - 3 {x}^{2} \times xyz \times 6 {y}^{3} \times {x}^{2} = \\ (- 3 \times6 ) \times {x}^{2 + 1 + 2} \times {y}^{1 + 3} \times z = \\ - 18 {x}^{5} {y}^{4} z$

$f)15 {x}^{3} \div5 {x}^{2} = \\ (15 \div 5) \times {x}^{3 - 2} = \\ 3x$

$g) - 8 {x}^{3} {y}^{2} \div 2 {x}^{2} y = \\ ( - 8 \div 2) \times {x}^{3 - 2} \times {y}^{2 - 1} = \\ - 4xy$

$h)10 {x}^{4} y {z}^{2} \div 5xyz = \\ (10 \div 5) \times {x}^{4 - 1} \times {y}^{1 -1 } \times {z}^{2 - 1} = \\ 2 {x}^{3} z$