Free Study Material

NCERT Solutions

NCERT Books

Revision Notes

Practice Problems

This is one of our many quizzes on Combining like terms. Click on this to access more such competitive quizzes on Algebraic Expressions.

Combining like terms Quiz 2

mathematics

 Solve $5( - x + y) + 2(x + {x^2}) - 9({x^2} + y) = 0$and choose the correct answer.

 Multiply the brackets with the number outside it and then combine the like terms. 

 Multiply the bracket and combine the like terms. We  get, $ \\ 5( - x + y) + 2(x + {x^2}) - 9({x^2} + y) = 0 \\   \Rightarrow  - 5x + 5y + 2x + 2{x^2} - 9{x^2} - 9y = 0 \\   \Rightarrow  - 5x + 2x + 5y - 9y + 2{x^2} - 9{x^2} = 0 \\   \Rightarrow  - 3x - 4y - 7{x^2} = 0 \\  $

 Tick the correct answer for $\dfrac{{{{(7x - 3y)}^2}}}{{{{(2 - 3y)}^2}}} = 1$

 Apply the formula ${(a - b)^2} = {a^2} + {b^2} - 2ab$.

 Applying the formula ${(a - b)^2} = {a^2} + {b^2} - 2ab$. Then combining the like terms together. We get, $ \\  \dfrac{{{{(7x - 3y)}^2}}}{{{{(2 - 3y)}^2}}} = 1 \\   \Rightarrow \dfrac{{49{x^2} + 9{y^2} - 42xy}}{{4 + 9{y^2} - 12y}} = 1 \\   \Rightarrow 49{x^2} + 9{y^2} - 42xy = 4 + 9{y^2} - 12y \\   \Rightarrow 49{x^2} + 9{y^2} - 9{y^2} - 42xy - 4 + 12y = 0 \\   \Rightarrow 49{x^2} - 42xy + 12y - 4 = 0 \\  $

 Choose the correct answer for $(2x - 3y)(2y + 6x)$

 Multiply the brackets and take all the like terms together and solve. 

 Multiply the brackets and combine the like terms together. We get, $ \\  (2x - 3y)(2y + 6x) \\   \Rightarrow 4xy + 12{x^2} - 6{y^2} - 18xy \\   \Rightarrow 4xy - 18xy + 12{x^2} - 6{y^2} \\   \Rightarrow  - 14xy + 12{x^2} - 6{y^2} \\  $

 Solve $\dfrac{{{{(9y + 2x - 8)}^{\frac{1}{2}}}}}{{{{(3x + 2y + 7)}^{\frac{1}{2}}}}} = \dfrac{2}{3}$and tick correct answer.

 Firstly squaring both sides we get, $ \\ \dfrac{{{{(9y + 2x - 8)}^{\frac{1}{2} \times 2}}}}{{{{(3x + 2y + 7)}^{\frac{1}{2} \times 2}}}} = {(\dfrac{2}{3})^2} \\   \Rightarrow \dfrac{{(9y + 2x - 8)}}{{(3x + 2y + 7)}} = \dfrac{4}{9} \\  $ Now simplifying the above equations and combining the like terms then we get, $ \\ \dfrac{{(9y + 2x - 8)}}{{(3x + 2y + 7)}} = \dfrac{4}{9} \\   \Rightarrow 81y + 18x - 72 = 12x + 8y + 28 \\   \Rightarrow 81y - 8y + 18x - 12x - 72 - 28 = 0 \\   \Rightarrow 73y + 6x - 100 = 0 \\  $

 Mark the correct answer for $6x - 2{y^2} - 9{x^2} - 2(3 - 2y) = 6(x - y)$

 Solve the brackets then combine the like terms. 

 First solve the brackets then combine the like terms. We get, $ \\  6x - 2{y^2} - 9{x^2} - 2(3 - 2y) = 6(x - y) \\   \Rightarrow 6x - 2{y^2} - 9{x^2} - 6 + 4y = 6x - 6y \\   \Rightarrow 6x - 6x - 2{y^2} - 9{x^2} - 6 + 4y + 6y = 0 \\   \Rightarrow  - 2{y^2} - 9{x^2} - 6 + 10y = 0 \\  $