Question

Find the product, using suitable properties: $\left( -59 \right)\times (-19)+57$

Answer 1

Hint: In this question we will use the rule of signs for multiplication and distributive property to solve given expression. According to the sign rule of multiplication in algebra, when two numbers, with like signs, are multiplied, the product will always be positive. Also, distributive property states that for three numbers a, b and c we can write $\left( a\times b+a\times c \right)=a\times \left( b+c \right)$ i.e. sum of products of a with and b and c is equal to the product of a with sum of b and c.

Complete step-by-step answer:
The expression in the equation is, $\left( -57 \right)\times \left( -19 \right)+57$ .
Here in the first term two numbers with like signs, that is negative, are multiplied. So, the resulting number will be positive. So, we can write:
$\left( -57 \right)\times \left( -19 \right)+57=57\times 19+57$
Also, any number when multiplied with 1 gives the same number. So, we can write $57$ as $57\times 1$.
So, we get \[\left( -57 \right)\times \left( -19 \right)+57=57\times 19+57\times 1\]
Here taking a = \[57\], b = \[19\] and c = $1$ , and applying the distributive property we get.
\[\left( -57 \right)\times \left( -19 \right)+57=57\times \left( 19+1 \right)\]
Adding \[19\] and 1, we get,
\[\left( -57 \right)\times \left( -19 \right)+57=57\times 20\]
Now multiplying 57 with 20, we get \[\left( -57 \right)\times \left( -19 \right)+57=1140\]
Hence, the value of expression is 1140.

Note:In this type of equation we try to make terms which ends with zeros as it makes multiplication easy and short. Carrying out multiplication without arranging terms can make the process bit complex.