Question

Using appropriate properties,find:
3/5×(-2/7)+3/2×1/5+(-2/7)×4/5
Please mention all the steps and properties used.

Answer 1

Answer:

-1÷10

Step-by-step explanation:

3/5×(-2/7)+3/2×1/5+(-2/7)×4/5=(-6/35)+3/10+(-8/35)

=(-12+21-16)/70=(-7/70)

=-1/10

Answer 2

Answer:

Required answer is $( - \frac{1}{10} )$

Step-by-step explanation:

Given,

$\frac{3}{5} \times ( - \frac{2}{7} ) + \frac{3}{2} \times \frac{1}{5} + ( - \frac{2}{7} ) \times \frac{4}{5}$

By Distributive property,

$x \times y + x \times z = x(y + z)$

So,

$( - \frac{2}{7} )( \frac{3}{5} + \frac{4}{5} ) + \frac{3}{2} \times \frac{1}{5} \\ = ( - \frac{2}{7} )( \frac{3 + 4}{5} ) + \frac{3}{2} \times \frac{1}{5} \\ = - \frac{2}{7} \times \frac{7}{5} + \frac{3}{10} \\ = - \frac{2}{5} + \frac{3}{10} \\ = \frac{ - 2 \times 2 + 3}{10} \\ = \frac{ - 4 + 3}{10} \\ = - \frac{1}{10}$

This is a problem of Algebra.

Some important Algebra formulas:

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

Know more about Algebra,

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