Question

Factorise x2y2(x-y)+y2z2(y-z)+z2x2(z-x)

Answer 1

Answer:

The given expression $x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x) =x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x)$

Step-by-step explanation:

An algebraic expression is a mathematical phrase that can contain numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, and division). Algebraic expressions are used to describe mathematical relationships and can be used to represent mathematical quantities.

Examples of algebraic expressions include: (2x + 3), (5y - 7), $(x^{2} -y^{2} )$

Arithmetic procedures can be used to join algebraic expressions to create more complicated expressions.

The given expression is $x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x)$

So, we have

$x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x)$

Expanding the terms, we have

$x^{3} y^{2} -x^{2} y^{3} +y^{3} z^{2} -z^{3} y^{2} +z^{3} x^{2} -x^{3} z^{2}$

Now, taking common from the terms, we have

$x^{3} (y^{2} -z^{2} )+y^{3} (z^{2} -x^{2} )+z^{3} (x^{2} -y^{2} )$

Now, we know an identity which is $(a^{2} -b^{2} ) = (a-b)(a+b)$

Using this in the aforementioned expression, we obtain

$x^{3} (y - z)(y +z) +y^{3} (z-x)(z+x) +z^{3} (x -y)(x+y)$

Therefore, The given expression$x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x) =x^{2} y^{2} (x -y) +y^{2} z^{2} (y -z) +z^{2} x^{2}(z -x)$

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