Subtract the sum of x2−3xy−y2 and 2x2+5xy−4y2 from 6x2−7xy+8y2

Question

asked Sep 21, 2021 113k views

2 Answers

Oana · Answer 1 · 2021-09-28T10:43:02+0000

Answer:

3x^2-9xy+13y^2

Explanation:

We begin with :
6x^2-7xy+8y^2-[(x^2-3xy-y^2)+(2x^2+5xy-4y^2)]

First, let us add the two portions within the brackets. To do this, we need to just combine the like terms

$6x^2-7xy+8y^2-[(x^2-3xy-y^2)+(2x^2+5xy-4y^2)]\\\\6x^2-7xy+8y^2-[3x^2+2xy-5y^2]$

Next, we need to distribute the negative to all the terms within the brackets

$6x^2-7xy+8y^2-[3x^2+2xy-5y^2]\\\\6x^2-7xy+8y^2-3x^2-2xy+5y^2$

Now we can combine the like terms again

$6x^2-7xy+8y^2-3x^2-2xy+5y^2\\\\3x^2-9xy+13y^2$