Question

Use the distributive property to rewrite and simplify $ \left( {5y - 3} \right)7 $ .

Answer 1

Hint: Distributive property is also known as the distributive law of multiplication. The expressions written in the form like $ a\left( {b + c} \right) $ are solved with the help of this property. It states that when the sum of the numbers given in the parenthesis is multiplied with the number given outside is same when the number given in the parenthesis is multiplied with the number outside individually and subtracted.

Complete step-by-step answer:
 In this problem, we have given an expression which we have to solve and simplify by using distributive property. The given expression is $ \left( {5y - 3} \right)7 $ and to solve this expression we need to multiply the $ 7 $ with $ 3 $ and then subtract it from the multiplication of $ 5y $ and $ 7 $ . Hence, the algebraic expression will become,
 $ \Rightarrow 7 \times 5y - 3 \times 7 $
When a number is multiplied with a variable, then the multiplication sign between them was removed. Now, on further solving, we get,
 $ \Rightarrow 35y - 21 $
Hence, the simplified expression for algebraic expression $ \left( {5y - 3} \right)7 $ by using distributive property is $ 35y - 21 $ .

Note: Here, we have used the distributive property, which can also be written as $ a\left( {b + c} \right) = a \times b + a \times c $ and to prove this property, let us take the algebraic expression mentioned above i.e, $ \left( {5y - 3} \right)7 $ and now, let us assume the value of y be $ 2 $ . Now, substitute the value of y in the algebraic expression,
 $ \Rightarrow \left( {5 \times 2 - 3} \right)7 $
On further solving, we get,
 $ \Rightarrow \left( {10 - 3} \right)7 $
Now, here are two ways of solving this:
First- We will subtract the terms and then multiplying it with number given outside,
 $ \Rightarrow 7 \times 7 = 49 $
Hence, the result with this method is $ 49 $ .
Second- We will multiply the numbers individually and then subtract,
 $ \Rightarrow \left( {10 \times 7 - 3 \times 7} \right) = 70 - 21 = 49 $
Hence, the result with this method is also $ 49 $ and hence, the distributive property is proved.