Question

How do you rewrite \[2b + 2c - 2d\] using the distributive property?

Answer 1

Hint: The distributive Property States that when a factor is multiplied by the sum or addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition. This property can be stated symbolically as: \[a\left( {b + c} \right) = ab + ac\].

Complete step by step answer:
Given,
\[2b + 2c - 2d\]
In which, we know that distributive property is stated symbolically as:
\[a\left( {b + c} \right) = ab + ac\]
Here, the monomial factor a is distributed, or separately applied, to each term of the binomial factor \[b + c\], resulting in the product \[ab + ac\].
To solve the given algebraic equation using the distributive property, we need to distribute (or multiply) the number with each term in the expression. Hence, we need combine like terms and solve by equivalent equations when necessary i.e., as given:
\[2b + 2c - 2d\]
As, there is a common term involved in the given equation i.e., 2, hence apply the distributive property by multiplying and dividing the equation by 2 as:
\[ = 2\left( {\dfrac{{2b}}{2} + \dfrac{{2c}}{2} - \dfrac{{2d}}{2}} \right)\]
We know that using distributive property multiplying the sum of two or more addends by a number will give the same result, hence as the denominator and numerator consists of same term; the equation is rewritten as:
\[2b + 2c - 2d = 2\left( {b + c - d} \right)\]

Note: The key point to note is that applying distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products and the distributive properties of addition and subtraction can be utilized to rewrite expressions for different purposes.