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This is one of our many quizzes on Addition properties. Click on this to access more such competitive quizzes on Integers.

Addition properties Quiz 2

mathematics

 Use distributive property to solve $3x + 2x\left( {x + 2} \right) - 6{x^2} + 5\left( {2{x^3} + 5{x^2} - 8} \right)$

 Apply Distributive property, and then combine and simplify the like terms.

 Given, $3x + 2x\left( {x + 2} \right) - 6{x^2} + 5\left( {2{x^3} + 5{x^2} - 8} \right)$ $ \\ $ Use distributive rule to remove parenthesis as: $ \\ 3x + 2{x^2} + 4x - 6{x^2} + 10{x^3} + 25{x^2} - 40 \\ $ Now, combine and simplify the like terms, $ \\ 10{x^3} + 21{x^2} + 7x - 40$

 Identify Distributive property from the following options 

 Use Distributive property of Addition to identify the equation i.e., $A \times \left( {B + C} \right) = A \times B + A \times C$.

 W.K.T in Distributive property, the sum of two numbers is multiplied by the third number is equal to the sum when each of the two numbers is multiplied to the third number. i.e., $A \times \left( {B + C} \right) = A \times B + A \times C$ , Hence applying this we need to find the given expression as: $ \\ A \times \left( {B + C} \right) = A \times B + A \times C \\ \Rightarrow 2 \times \left( {5 + 7} \right) = 2 \times 5 + 2 \times 7$

 Find the value of $x$ in$5\left( {x - 2} \right) = 20$

 Use Distributive property of Addition to simplify.

 Distributive property of Addition is: $A + \left( {B + C} \right) = \left( {A + B} \right) + C$,  $ \\ $ Given $5\left( {x - 2} \right) = 20$ $ \\ $ Applying distributive property, we have: $ \\ 5\left( x \right) - 5\left( 2 \right) = 20 \\ \Rightarrow 5x - 10 = 20 \\ $ Add 10 on both sides of the equation as: $\\ 5x - 10 + 10 = 20 + 10 \\ \Rightarrow 5x = 20 + 10 \\ \Rightarrow 5x = 30 \\ \Rightarrow x = \dfrac{{30}}{5} \\ \Rightarrow x = 6$

 To evaluate the given expression we need to distribute the terms and simplify it.

 Given, ${\left( {5x + 5} \right)^2}$, $ \\ $ Apply distributive property to simplify i.e., $ \\ {\left( {5x + 5} \right)^2} = \left( {5x + 5} \right)\left( {5x + 5} \right) \\ $ Multiplying the terms, we have: $ \\ {\left( {5x + 5} \right)^2} = 25{x^2} + 25x + 25x + 25 \\ $ Evaluating the terms, we get: $ \\ {\left( {5x + 5} \right)^2} = 25{x^2} + 50x + 25$

 Solve using distributive property $2y + 5\left( {y - 2} \right) = 60$

 Use Distributive property of Addition and combine the like terms, to find the value of $y$.

 Given, $2y + 5\left( {y - 2} \right) = 60 \\ \Rightarrow 2y + 5y - 10 = 60 \\ $ Add $10$ on both sides of the expression we get: $ \\ 2y + 5y - 10 + 10 = 60 + 10 \\ \Rightarrow 2y + 5y = 60 + 10 \\ \Rightarrow 7y = 70 \\ \Rightarrow y = \dfrac{{70}}{7} \\ \Rightarrow y = 10$