How Do I Solve These? "Simplify The Following... (2a + b)² - (b - 2a)²"

[Saheed204]

How Do I Solve These? "Simplify The Following... (2a + b)² - (b - 2a)²"

Simplify The Following...


(2a + b)² - (b - 2a)²

 

[Deleted member 4993]

Simplify The Following...


(2a + b)² - (b - 2a)²

Hint: Use (x + y)² = x² + 2*x*y + y²

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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[HallsofIvy]

It may be simpler, I think, to use the fact that $\displaystyle x^2- y^2= (x- y)(x+ y)$. Here, $\displaystyle x= 2a+ b$ and $\displaystyle y= b- 2a$. So what are x- y and x+ y?

 

[lookagain]

Simplify The Following...


(2a + b)² - (b - 2a)²

Because of the even exponent, you can rewrite it as this first:

(2a + b)² - (2a - b)²

 

[Deleted member 4993]

It may be simpler, I think, to use the fact that $\displaystyle x^2- y^2= (x- y)(x+ y)$. Here, $\displaystyle x= 2a+ b$ and $\displaystyle y= b- 2a$. So what are x- y and x+ y?

It is simpler - I was hoping that the OP will come to that realization once the "simplification" process started.