Question

What should be subtracted from $ 5{x^2} + 2x - 5 $ to get $ 3xy + 4x - 5. $

Answer 1

Hint: Here we will assume the given expression and the result we want. Will frame the equation accordingly and then will simplify for the resultant required answer. Always remember when you move any term from one side to another, the sign of the term also changes. Positive terms become negative and negative terms become positive. Be careful about the sign.

Complete step-by-step answer:
Let us assume that –
 $ p(x) = 5{x^2} + 2x - 5 $
And $ q(x) = 3xy + 4x - 5. $
Let the terms/ term to be subtracted be equal to “A”
Therefore, $ p(x) - A = q(x) $
Place the values in the above expression –
 $ \Rightarrow 5{x^2} + 2x - 5 - A = 3xy + 4x - 5 $
Take all the terms on one side of the equation. Take “A” on the right hand side of the equation and other terms on the right to the left of the equation. Remember when you move a term from one side to another, the sign of the term also changes. Positive term becomes negative and negative term becomes positive.
 $ \Rightarrow 5{x^2} + 2x - 5 - 3xy - 4x + 5 = A $
It can be re-written as –
 $ \Rightarrow A = 5{x^2} + 2x - 5 - 3xy - 4x + 5 $
Make the pair of like terms in the above equation –
 $ \Rightarrow A = 5{x^2} - 3xy - \underline {4x + 2x} - \underline {5 + 5} $
Like terms with equal value and opposite signs cancel each other. Also, when you add one positive term with one negative term you have to subtract and sign the larger digit. Simplify the above equation.
 $ \Rightarrow A = 5{x^2} - 3xy - 2x $
Hence, $ 5{x^2} - 3xy - 2x $ should be subtracted from $ 5{x^2} + 2x - 5 $ to get $ 3xy + 4x - 5. $
So, the correct answer is “$ 5{x^2} - 3xy - 2x $”.

Note: While doing simplification remember the golden rules-
A.Addition of two positive terms gives the positive term
B.Addition of one negative and positive term, you have to do subtraction and give sign of bigger numbers, whether positive or negative.
C.Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.