Question

Verify the following:
a) $18 \times [7+(-3)]=[18 \times 7]+[18 \times (-3)]$
b) $(-21) \times [(-4)+(-6)]=[(-21)\times (-4)]+[(-21) \times (-6)]$

Answer 1

Hint:
The property used in the question is the distributive property of multiplication. We will first solve the left hand side of the equation and then we will solve the right hand side of the equation such that the values of right hand side expression and left hand side expression are same or equal and thus the equation will get verified.

Complete step by step solution:
$18\times \left[ 7+\left( -3 \right) \right]=\left[ 18\times 7 \right]+\left[ 18\times \left( -3 \right) \right]$
First we will solve the left hand side of the given equation.
Left hand side expression is $18\times \left[ 7+\left( -3 \right) \right]$ or
$LHS=18\times \left[ 7+\left( -3 \right) \right]$
First we will add the terms inside the bracket.
$LHS=18\times \left( 4 \right)$
Multiplying the18 with 4, we get
$LHS=72$
Now, we will solve the right hand side of the given equation.
Left hand side expression is $\left[ 18\times 7 \right]+\left[ 18\times \left( -3 \right) \right]$ or
$RHS=\left[ 18\times 7 \right]+\left[ 18\times \left( -3 \right) \right]$
First we will multiply the terms inside the brackets.
$RHS=126+\left( -54 \right)$
Opening the bracket, we get
$RHS=126-54$
Subtracting 54 from 126, we get
$RHS=72$
We can see that the value of $LHS$ and $RHS$ are equal i.e.
$LHS=RHS=72$
Hence, verified.
$\left( -21 \right)\times \left[ \left( -4 \right)+\left( -6 \right) \right]=\left[ \left( -21 \right)\times \left( -4 \right) \right]+\left[ \left( -21 \right)\times \left( -6 \right) \right]$
First we will solve the left hand side of the given equation.
Left hand side expression is $\left( -21 \right)\times \left[ \left( -4 \right)+\left( -6 \right) \right]$ or
$LHS=\left( -21 \right)\times \left[ \left( -4 \right)+\left( -6 \right) \right]$
First we will add the terms inside the bracket.
$LHS=\left( -21 \right)\times \left( -10 \right)$
Multiplying the-21 with -10, we get
$LHS=210$
Now, we will solve the right hand side of the given equation.
Left hand side expression is $\left[ \left( -21 \right)\times \left( -4 \right) \right]+\left[ \left( -21 \right)\times \left( -6 \right) \right]$ or
$RHS=\left[ \left( -21 \right)\times \left( -4 \right) \right]+\left[ \left( -21 \right)\times \left( -6 \right) \right]$
First we will multiply the terms inside the brackets.
$RHS=84+126$
On adding 84 and 126, we get
$RHS=210$
We can see that the value of $LHS$ and $RHS$ are equal i.e.
$LHS=RHS=210$
Hence, verified.

Note:
Here distributive property of multiplication has been used here i.e. in this question we have verified distributive property of multiplication. Distributive property of multiplication states that if $a$, $b$ and $c$ are three real numbers then according to this property, $a\left( b+c \right)=a.b+a.c$.