Question

Evaluate using property: \[56 * \left( { - 42} \right) + 56 * \left( { - 58} \right)\] .

Answer 1

Hint: In these questions use the distributive property \[\left( {x * a} \right) + (x * b) = x(a + b)\] as it is given \[x = 56\], \[a = - 42\] and \[b = - 58\]. We can use these values in the given formula to evaluate.
Formula Used: Here, we are using the distributive property \[\left( {x * a} \right) + (x * b) = x(a + b)\].

Complete step-by-step answer:
As, we are using one of the properties by observing the given question \[56 * \left( { - 42} \right) + 56 * \left( { - 58} \right)\] . We are able to see that \[\left( {x * a} \right) + (x * b)\] from the given statement. So, now we will use the property to evaluate the answer.
Now, let us calculate x , a , b .
So, \[56 * \left( { - 42} \right) + 56 * \left( { - 58} \right)\] from this statement 56 is a common part which is x in the formula.
\[\therefore x = 56\]
Now from \[56 * \left( { - 42} \right) + 56 * \left( { - 58} \right)\]. This statement we can calculate a and b also . So, here a comes out to be -42 and b comes out to be -58. \[\therefore a = - 42\] and \[\therefore b = - 58\] .
Now, Putting the values of x , a , b in the formula . We can calculate the result.
As we know the distributive property : \[\left( {x * a} \right) + (x * b) = x(a + b)\]
Implement it as, \[56 * \left( { - 42} \right) + 56 * \left( { - 58} \right) = 56(\left( { - 42} \right) + \left( { - 58} \right))\]
Calculating right hand side,
\[ \Rightarrow x(a + b)\]
\[ \Rightarrow 56(\left( { - 42} \right) + \left( { - 58} \right))\]
Now, we will open the brackets and change signs wherever needed.
\[ \Rightarrow 56( - 42 - 58)\]
Here, we will add 42 and 58 but we will put the negative sign.
\[ \Rightarrow 56( - 100)\]
Now, we will multiply 100 by 56 and put the negative sign as in multiplication \[positive * negative = negative\].
So, we get \[ - 5600\]
\[\therefore 56 * \left( { - 42} \right) + 56 * \left( { - 58} \right) = - 5600\]
Additional Information: Distributive property means we can multiply a sum by a number is the same as multiplying every addend by a number and then adding its product.

Note: We must know the properties very carefully so that by the given statement it can be observed which property is to be applied. Applying the wrong property can affect the final result of the problem. As we solve problems we should check previous steps also for confirmation.