(a+b)^2–(b+c)^2 as a product of two polynomials

Hey there!!

In order to solve this problem, we will need to use the identity a² - b²

∴ a² - b² = ( a + b ) ( a - b )

According to the question,

a = a + b

b = b + c

( a + b )² - ( b + c )²

... ( a + b + b + c ) ( a + b - b - c )

... ( a + 2b + c ) ( a - c )

Now, we will need to solve this using distributive property.

Distribute a with a , 2b , c and distribute -c with a , 2b and c and then combine all the like terms.

... ( a² + 2ab + ac ) + ( -ac - 2bc - c² )

... ( a² + 2ab + ac - ac - 2bc - c² )

... ( a² + 2ab - bc - c² )

Hope my answer helps!!

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