Question

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Answer 1

a)

$7 x^{2} y^{2} - 21 x y^{2} z + 7 x y z - 14 x y = 7 x y . x y - 7 x y . 3 y z + 7 x y . z + 7 x y . 2 = 7 x y (x y - 3 y z + z + 2) b, a^{3} x^{2} y - \frac{5}{2} a^{3} x^{4} + \frac{3}{2} a^{4} x^{2} y = a^{3} x^{2} . (y - \frac{5}{2} x^{2} + \frac{3}{2} a . y) c, - 16 a^{4} b^{6} - 24 a^{5} b^{5} - 9 a^{6} b^{4} = - a^{4} . b^{4} . (16 b^{2} + 24 a b + 9 a^{2}) = - a^{4} . b^{4} . [{(4 b)}^{2} + 2.3.4 a b + {(3 a)}^{2}] = - a^{4} . b^{4} . {(4 b + 3 a)}^{2}$

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Answer 2

a)

$7 x^{2} y^{2} - 21 x y^{2} z + 7 x y z - 14 x y = 7 x y . x y - 7 x y . 3 y z + 7 x y . z + 7 x y . 2 = 7 x y (x y - 3 y z + z + 2) b, a^{3} x^{2} y - \frac{5}{2} a^{3} x^{4} + \frac{3}{2} a^{4} x^{2} y = a^{3} x^{2} . (y - \frac{5}{2} x^{2} + \frac{3}{2} a . y) c, - 16 a^{4} b^{6} - 24 a^{5} b^{5} - 9 a^{6} b^{4} = - a^{4} . b^{4} . (16 b^{2} + 24 a b + 9 a^{2}) = - a^{4} . b^{4} . [{(4 b)}^{2} + 2.3.4 a b + {(3 a)}^{2}] = - a^{4} . b^{4} . {(4 b + 3 a)}^{2}$

Answer 3

a.

$7 x^{2} y^{2} - 21 x y^{2} z + 7 x y z - 14 x y = 7 x y . x y - 7 x y . 3 y z + 7 x y . z - 7 x y . 2 = 7 x y (x y - 3 y z + z - 2)$

b.

$a^{3} x^{2} y - \frac{5}{2} a^{3} x^{4} + \frac{3}{2} a^{4} x^{2} y = a^{3} x^{2} . y - a^{3} x^{2} . (\frac{5}{2} x^{2}) + a^{3} x^{2} . (\frac{3}{2} a y) = a^{3} x^{2} (y - \frac{5}{2} x^{2} + \frac{3}{2} a y)$

c.

$- 16 a^{4} b^{6} - 24 a^{5} b^{5} - 9 a^{6} b^{4} = - a^{4} b^{4} . (16 b^{2}) - a^{4} b^{4} . (24 a b) - a^{4} b^{4} . (9 a^{2}) = - a^{4} b^{4} (16 b^{2} + 24 a b + 9 a^{2}) = - a^{4} b^{4} [{(4 b)}^{2} + 2.4 b . 3 a + {(3 a)}^{2}] = - a^{4} b^{4} {(3 a + 4 b)}^{2}$

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Answer 4

a.

$7 x^{2} y^{2} - 21 x y^{2} z + 7 x y z - 14 x y = 7 x y . x y - 7 x y . 3 y z + 7 x y . z - 7 x y . 2 = 7 x y (x y - 3 y z + z - 2)$

b.

$a^{3} x^{2} y - \frac{5}{2} a^{3} x^{4} + \frac{3}{2} a^{4} x^{2} y = a^{3} x^{2} . y - a^{3} x^{2} . (\frac{5}{2} x^{2}) + a^{3} x^{2} . (\frac{3}{2} a y) = a^{3} x^{2} (y - \frac{5}{2} x^{2} + \frac{3}{2} a y)$

c.

$- 16 a^{4} b^{6} - 24 a^{5} b^{5} - 9 a^{6} b^{4} = - a^{4} b^{4} . (16 b^{2}) - a^{4} b^{4} . (24 a b) - a^{4} b^{4} . (9 a^{2}) = - a^{4} b^{4} (16 b^{2} + 24 a b + 9 a^{2}) = - a^{4} b^{4} [{(4 b)}^{2} + 2.4 b . 3 a + {(3 a)}^{2}] = - a^{4} b^{4} {(3 a + 4 b)}^{2}$

Answer 5

a,7xy(xy-3yz+z-2)

b, $a^{3} x^{2} y (1 - \frac{5}{2} x^{2} + \frac{3}{2} a)$

c,−16a^4b^6−24a^5b^5−9a^6b^4−16a^4b^6−24a^5b^5−9a^6b^4

−a^4b^4(16b^2+24ab+9a^2)=−a^4b^4(16b^2+24ab+9a^2)

−a^4b^4(3a+4b)^2

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