How do you multiply $3 x^{2} y^{2} z (7 x^{2} + 2 y + z + 4 w)$ $3x^2y^2z(7x^2+2y+z+4w)$ ?

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How do you multiply $3 x^{2} y^{2} z (7 x^{2} + 2 y + z + 4 w)$ $3x^2y^2z(7x^2+2y+z+4w)$ ?

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Answer 1 · 2017-04-27T18:29:10

$21 x^{4} y^{2} z + 6 x^{2} y^{3} z + 3 x^{2} y^{2} z^{2} + 12 x^{2} y^{2} z w$ $21x^4y^2z+6x^2y^3z+3x^2y^2z^2+12x^2y^2zw$

Explanation:

Multiply each part of $7 x^{2} + 2 y + z + 4 w$ $7x^2+2y+z+4w$ by $3 x^{2} y^{2} z$ $3x^2y^2z$
$3 x^{2} y^{2} z (7 x^{2}) = 21 x^{4} y^{2} z$ $3x^2y^2z(7x^2)=21x^4y^2z$
$3 x^{2} y^{2} z (2 y) = 6 x^{2} y^{3} z$ $3x^2y^2z(2y)=6x^2y^3z$
$3 x^{2} y^{2} z (z) = 3 x^{2} y^{2} z^{2}$ $3x^2y^2z(z)=3x^2y^2z^2$
$3 x^{2} y^{2} z (4 w) = 12 x^{2} y^{2} z w$ $3x^2y^2z(4w)=12x^2y^2zw$

Then you add each part to get
$21 x^{4} y^{2} z + 6 x^{2} y^{3} z + 3 x^{2} y^{2} z^{2} + 12 x^{2} y^{2} z w$ $21x^4y^2z+6x^2y^3z+3x^2y^2z^2+12x^2y^2zw$

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How do you multiply $3 x^{2} y^{2} z (7 x^{2} + 2 y + z + 4 w)$ $3x^2y^2z(7x^2+2y+z+4w)$ ?

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Explanation:

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How do you multiply $3 x^{2} y^{2} z (7 x^{2} + 2 y + z + 4 w)$ $3x^2y^2z(7x^2+2y+z+4w)$ ?