Question

this question please​

Answer 1

Answer:

a) 9x² - 3y² + z²

b) x - y

Step-by-step explanation:

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Answer 2

Answer of part a) $(3x + 3y+z) (3x - 3y-z)$

Answer of part b) $8xy(x^2+y^2)$

Step-by-step explanation:

For both the parts the identity used is $a^2 -b^2 = (a+b) (a-b)$

Let us solve stepwise:

a) $9x^2 -(3y+z)^2$

Making it in the form of the identity $a^2 -b^2 = (a+b) (a-b)$, we obtain

= $(3x)^2 -(3y+z)^2$

= $[3x + (3y+z)] [3x - (3y+z)]$      

Opening the brackets and solving,

= $(3x + 3y+z) (3x - 3y-z)$

b) $(x+y)^4 - (x-y)^4$

To apply the identity $a^2 -b^2 = (a+b) (a-b)$, first we convert the power term to 2, as follows,

= $[(x+y)^2]^2 - [(x-y)^2]^2$

Now, applying the identity,

= $[(x+y)^2 + (x-y)^2] [(x+y)^2 - (x-y)^2]$

The terms in the parenthesis can be expanded using the identities$(a+b)^2 = a^2 + b^2 + 2ab$ and $(a-b)^2 = a^2 + b^2 - 2ab$.

We get,

= $[(x^2 + y^2 +2xy) + (x^2 + y^2 -2xy)] [(x^2 + y^2 +2xy) - (x^2 + y^2 -2xy)]$

Opening the brackets, and solving

= $[x^2 + y^2 + 2xy + x^2 + y^2 - 2xy ][x^2 + y^2 +2xy - x^2 - y^2 + 2xy]$

= $[2x^2 + 2y^2 ][4xy]$

= $8xy(x^2+y^2)$