Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
11.\\
7{x^2} - 7xy - 4x + 4y\\
= 7x\left( {x - y} \right) - 4\left( {x - y} \right)\\
= \left( {x - y} \right)\left( {7x - 4} \right)\\
12.\\
x(2x - 7) - (4x - 14)\\
= x\left( {2x - 7} \right) - 2\left( {2x - 7} \right)\\
= \left( {2x - 7} \right)\left( {x - 2} \right)\\
13.\\
{x^4} + 3{x^3} - 9x - 9\\
= {x^4} - 9 + 3{x^3} - 9x\\
= \left( {{x^2} - 3} \right)\left( {{x^2} + 3} \right) + 3x\left( {{x^2} - 3} \right)\\
= \left( {{x^2} - 3} \right)\left( {{x^2} + 3 + 3x} \right)\\
= \left( {x - \sqrt 3 } \right)\left( {x + \sqrt 3 } \right)\left( {{x^2} + 3x + 3} \right)\\
15.12{a^2} - 6ab + 3{b^2} - 6ab\\
= 12{a^2} - 12ab + 3{b^2}\\
= 3\left( {4{a^2} - 4ab + {b^2}} \right)\\
= 3{\left( {2a - b} \right)^2}
\end{array}\]

Answer 2

$11, 7 x^{2} - 7 x y - 4 x + 4 y = (7 x^{2} - 7 x y) - (4 x - 4 y) = 7 x . (x - y) - 4 . (x - y) = (x - y) (7 x - 4) 12, x (2 x - 7) - (4 x - 14) = x (2 x - 7) - 2 . (2 x - 7) = (2 x - 7) (x - 2) 13, x^{4} + 3 x^{3} - 9 x - 9 = x^{3} . (x + 1) - 9 (x + 1) = (x + 1) (x^{3} - 9) 14, 12 a^{2} - 6 a b + 3 b^{2} - 6 a b = 12 a^{2} - 12 a b + 3 b^{2} = 3 . (4 a^{2} - 4 a b + b^{2}) = 3 {(2 a - b)}^{2}$ .

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Answer 3

$11, 7 x^{2} - 7 x y - 4 x + 4 y = (7 x^{2} - 7 x y) - (4 x - 4 y) = 7 x . (x - y) - 4 . (x - y) = (x - y) (7 x - 4) 12, x (2 x - 7) - (4 x - 14) = x (2 x - 7) - 2 . (2 x - 7) = (2 x - 7) (x - 2) 13, x^{4} + 3 x^{3} - 9 x - 9 = x^{3} . (x + 1) - 9 (x + 1) = (x + 1) (x^{3} - 9) 14, 12 a^{2} - 6 a b + 3 b^{2} - 6 a b = 12 a^{2} - 12 a b + 3 b^{2} = 3 . (4 a^{2} - 4 a b + b^{2}) = 3 {(2 a - b)}^{2}$ .

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