# Ex 12.2 Q5 Algebraic-Expressions Solutions NCERT Maths Class 7

## Question

What should be taken away from \(3x^2 – 4y^2 + 5xy + 20\) to obtain \(– x^2 – y^2 + 6xy + 20?\)

## Text Solution

**What is known?**

we know that arithmetic operation will be applied.

**Reasoning:**

In this question basic concept of arithmetic operations is applied. We are given two terms and asked what should be subtracted from one term to get the required answer. For this we will subtract the given answer from the 1^{st} term to get what should be subtracted. E.g: what should be subtracted from \(5\) to get \(3.\) We will subtract \(3\) from \(5.\)

**Steps:**

1^{st} term \(= 3x^2 – 4y^2 + 5xy + 20\)

Answer term \(= \, – x^2 – y^2 + 6xy + 20\)

2^{nd} term = 1^{st} term – Answer

2^{nd} term

\[\begin{align}&\!\!\!\!\!\!= \!3x^2\! –\! 4y^2 \!+\! 5xy \!+ \!20 \!–\! (\!– \!x^2\! –\! y^2\! + \!6xy \!+ \!20)\\&\!\!\!\!\!\!= \!3{x^2}\!\!-\!4{y^2} \!+ \!5xy \!+\! 20 \!+\! {x^2} \!\!+ \!{y^2} \!-\! 6xy\! -\! 20\\&\!\!\!\!\!\! = \!4{x^2} \!-\! 3{y^2} \!- \!xy\end{align}\]* *