Question

Substract 4p2+5q2-6r2+7 from 3p2-4q2-5r2-6​

Answer 1

Hey mate .......☺
The answer will be.....

$\small{\bold{\red{-1p^2-9q^2+r^2-13}}}$

I HOPE IT IS HELPFUL FOR YOU....☺✌☺

Answer 2

$\Huge{\boxed{\pink{\mathbb{QUESTION}}}}$

Subtract : $4p^2 + 5q^2 - 6r^2 + 7\:from\: 3p^2 - 4q^2 - 5r^2 - 6$

$\Huge{\boxed{\purple{\mathcal{ANSWER}}}}$

We can subtract it by various methods. But we'll subtract it by using 'grouping the terms methods'.

In this method, we can add or subtract by grouping the same term which has same variable and same power (or) exponent.

$\bold{For\:eg,\:1\::\:-}$

Subtract : - 5p from 2p

Answer : - Now we'll group them as they are having same variable 'p'.

=> (5p - 2p)

=> 3p

Here, the power (or) exponent was 1. Let's look for another example with power 2.

$\bold{For\:eg,\:2\::\:-}$

Subtract : - $5p^2\:from\:3p^2$

Answer : - As they both are having same variable 'p' and same power (or) exponent '2', we can group them.

=> $(5p^2 - 2p^2)$

=> $3p^2$

Here, the power and the variable were same. But what will happen when there are two different variables? Let's understand it with an example.

$\bold{For\:eg,\:3\::\:-}$

Subtract : - $5p - 3q$

Answer : - Here, the variable is not same. Therefore, we can't group them. It will remain as it is. Like,

=> (5p - 3q)

=> 5p - 3q

But what will happen if both the variables and the power are not same? Let's understand with a same example.

$\bold{For\:eg,\:4\::\:-}$

Subtract : - $5p^2 - 3q^2$

Answer : - As both the variable and terms are not equal we can't group them. Then they will remain as same. Like,

=> $(5p^2 - 3q^2)$

=> $5p^2 - 3q^2$

Here, $5p^2\:and\: - 3q^2$ are unlike terms and thus we can subtract them.

Unlike terms are the terms which neither have same equal variables nor equal powers.

But in example 1, 5p and 2p are like terms. And thus, we are abled to subtract them.

Like terms are the terms which have both same variable and power.

Now, we have learn everything, and we can come up with our questions, that is,

Subtract : $4p^2 + 5q^2 - 6r^2 + 7\:from\: 3p^2 - 4q^2 - 5r^2 - 6$

=> By using grouping method,

=> $(4p^2 - 3p^2) + (5q^2 - 4q^2) + (6r^2 - 5r^2) + (7 - 6)$

=> $(p^2) + (q^2) + (r^2) + (1)$

=> $p^2 + q^2 + r^2 + 1$

$\Huge{\boxed{\red{Answer\:=\:p^2 +q^2 + r^2 + 1}}}$