Question

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Answer 1

$64 x^{6} + 0, 027 y^{9} = {(4 x^{2})}^{3} + {(0, 3 y^{3})}^{3} = (4 x^{2} + 0, 3 y^{3}) [{(4 x^{2})}^{2} - (4 x^{2}) . (0, 3 y^{3}) + {(0, 3 y^{3})}^{2}] = (4 x^{2} + 0, 3 y^{3}) (16 x^{4} - 1, 2 x^{2} y^{3} + 0, 09 y^{6})$

${(x + 5)}^{2} + 2 (x + 5) (x - y) + {(x - y)}^{2} = {[(x + 5) + (x - y)]}^{2} = {(2 x - y + 5)}^{2}$

$0, 64 + 64 x^{2} - 12, 8 x = {(8 x)}^{2} - 2.8 x . 0, 8 + {(0, 8)}^{2} = {(8 x - 0, 8)}^{2}$

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Answer 2

$64 x^{6} + 0, 027 y^{9} = {(4 x^{2})}^{3} + {(0, 3 y^{3})}^{3} = (4 x^{2} + 0, 3 y^{3}) [{(4 x^{2})}^{2} - (4 x^{2}) . (0, 3 y^{3}) + {(0, 3 y^{3})}^{2}] = (4 x^{2} + 0, 3 y^{3}) (16 x^{4} - 1, 2 x^{2} y^{3} + 0, 09 y^{6})$

${(x + 5)}^{2} + 2 (x + 5) (x - y) + {(x - y)}^{2} = {[(x + 5) + (x - y)]}^{2} = {(2 x - y + 5)}^{2}$

$0, 64 + 64 x^{2} - 12, 8 x = {(8 x)}^{2} - 2.8 x . 0, 8 + {(0, 8)}^{2} = {(8 x - 0, 8)}^{2}$

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Answer 3

a,

$64 x^{6} + 0, 027 y^{9} = {(4 x^{2})}^{3} + {(0, 3 y^{3})}^{3} = (4 x^{2} + 0, 3 y^{3}) . [{(4 x^{2})}^{2} - 4 x^{2} . 0, 3 y^{3} + {(0, 3 y^{3})}^{2}] = (4 x^{2} + 0, 3 y^{3}) . (16 x^{4} - 1, 2 x^{2} y^{3} + {0, 09 y}^{6}) b, {(x + 5)}^{2} + 2 (x + 5) (x - y) + {(x - y)}^{2} = {(x + 5 + x - y)}^{2} = {(2 x - y + 5)}^{2} c, 0, 64 + 64 x^{2} - 12, 8 x = {(8 x)}^{2} - 2.8 x . 0, 8 + {(0, 8)}^{2} = {(8 x - 0, 8)}^{2} i) (4 x^{2} + 1 - 4 x) + (9 + x^{2} + 6 x) + (4 x - 2) (x + 3) = [{(2 x)}^{2} - 2.2 x + 1] + (x^{2} + 2.3 x + 3^{2}) + 2 . (2 x - 1) . (x + 3) = {(2 x - 1)}^{2} + 2 . (2 x - 1) . (x + 3) + {(x + 3)}^{2} = {(2 x - 1 + x + 3)}^{2} = (3 x + 2)^{2}$

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Answer 4

a,

$64 x^{6} + 0, 027 y^{9} = {(4 x^{2})}^{3} + {(0, 3 y^{3})}^{3} = (4 x^{2} + 0, 3 y^{3}) . [{(4 x^{2})}^{2} - 4 x^{2} . 0, 3 y^{3} + {(0, 3 y^{3})}^{2}] = (4 x^{2} + 0, 3 y^{3}) . (16 x^{4} - 1, 2 x^{2} y^{3} + {0, 09 y}^{6}) b, {(x + 5)}^{2} + 2 (x + 5) (x - y) + {(x - y)}^{2} = {(x + 5 + x - y)}^{2} = {(2 x - y + 5)}^{2} c, 0, 64 + 64 x^{2} - 12, 8 x = {(8 x)}^{2} - 2.8 x . 0, 8 + {(0, 8)}^{2} = {(8 x - 0, 8)}^{2} i) (4 x^{2} + 1 - 4 x) + (9 + x^{2} + 6 x) + (4 x - 2) (x + 3) = [{(2 x)}^{2} - 2.2 x + 1] + (x^{2} + 2.3 x + 3^{2}) + 2 . (2 x - 1) . (x + 3) = {(2 x - 1)}^{2} + 2 . (2 x - 1) . (x + 3) + {(x + 3)}^{2} = {(2 x - 1 + x + 3)}^{2} = (3 x + 2)^{2}$

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