Question

From the sum of 2y2+3yz and - y 2+yz – z 2 , subtract the sum of 3y2+z2 and y2+yz

Answer 1

Answer:

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Step-by-step explanation:

Given to us ,two sets of expressions. The first set contains 2y2+3yz,−y2−yz−z2 and yz+2z2 and these are to be added. The second set contains 3y2−z2 and −y2+yz+z2 to be added.

Firstly, let us add the expressions in the first set. This can be written as follows.

⇒2y2+3yz+(−y2−yz−z2)+yz+2z2

By removing the brackets, we get

2y2+3yz−y2−yz−z2+yz+2z2

Now we know that terms with the same variables and powers can be added or subtracted so let us segregate all the y terms, z terms and yz terms together.

This expression now becomes

2y2−y2+3yz−yz+yz−z2+2z2

Now, we can take common terms out and write the coefficients together.

⇒y2(2−1)+yz(3−1+1)+z2(−1+2)

By solving this, we get (1)y2+(3)yz+(1)z2

So now this expression becomes y2+3yz+z2

Similarly, we can add the expressions of the other set 3y2−z2 and −y2+yz+z2

⇒3y2−z2−y2+yz+z2

Let us segregate similar terms together to get 3y2−y2+yz−z2+z2

Taking common variables out and writing coefficients together

⇒(3−1)y2+yz+(−1+1)z2

By solving we get 2y2+yz

Now, we have to subtract the second expression from the first.

We can write this as

⇒y2+3yz+z2−(2y2+yz)

By removing the bracket we get y2+3yz+z2−2y2−yz

We follow the same steps and write this as

⇒(1−2)y2+(3−1)yz+z2

On solving, we get −y2+2yz+z2

Therefore the answer is 2yz+z2−y2