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a) Ta có: \(-2xy^2\cdot\left(x^3y-2x^2y^2+5xy^3\right)\)
\(=-2x^4y^3+4x^3y^4-10x^2y^5\)
b) Ta có: \(\left(-2x\right)\cdot\left(x^3-3x^2-x+1\right)\)
\(=-2x^4+6x^3+2x^2-2x\)
c) Ta có: \(3x^2\left(2x^3-x+5\right)\)
\(=6x^5-3x^3+15x^2\)
d) Ta có: \(\left(-10x^3+\frac{2}{5}y-\frac{1}{3}z\right)\cdot\left(-\frac{1}{2}xy\right)\)
\(=5x^4y-\frac{1}{5}xy^2+\frac{1}{6}xyz\)
e) Ta có: \(\left(3x^2y-6xy+9x\right)\cdot\left(-\frac{4}{3}xy\right)\)
\(=-4x^3y^2+8x^2y^2-12x^2y\)
f) Ta có: \(\left(4xy+3y-5x\right)\cdot x^2y\)
\(=4x^3y^2+3x^2y^2-5x^3y\)
a, P + 3x\(^{^2}\) - 4xy = 6y\(^{^2}\) - 9xy + x\(^2\)
=> P = 6y\(^2\)- 9xy + x\(^2\)+ 4xy - 3x\(^2\)= 6y\(^2\)- 5xy - 2x\(^2\)
=> P = 6y\(^2\) - 5xy - 2x\(^2\)
b,
4y\(^2\) - 8xy - P = 5x\(^2\) - 12xy + 4y\(^2\)
=> P = 4y\(^2\) - 8xy - 5x\(^2\) + 12xy - 4y\(^2\) = 4xy - 5x\(^2\)
=> P = 4xy - 5x\(^2\)
c,
P - ( x\(^2\) - 2y\(^2\) + 3z\(^2\) ) + 3x\(^2\) - y\(^2\) + 2z\(^2\)= 2x\(^2\) - 3y\(^2\) -z\(^2\)
= P + 2x\(^2\) + y\(^2\) - z\(^2\) = 2x\(^2\) - 3y\(^2\) - z\(^2\)
=> P = 2x\(^2\) - 3y\(^2\) - z\(^2\) - 2x\(^2\) - y\(^2\) + z\(^2\)
=> P = -2y\(^2\)
\(C=\frac{7}{9}x^3y^2\left(\frac{6}{11}axy^3\right)+\left(-5bx^2y^4\right)\left(\frac{-1}{2}axz\right)+ax\left(x^2y\right)^3\)
\(\Rightarrow C=\frac{42}{9}ax^4y^5+\frac{5}{2}abx^3y^4z+ax\left(x^6y^3\right)\)
\(\Rightarrow C=\frac{42}{9}ax^4y^5+\frac{5}{2}abx^3y^4z+ax^7y^3\)
\(D=\frac{\left(3x^4y^4\right)^2\left(\frac{6}{11}x^3y\right)\left(8x^{n-7}\right)\left(-2x^{7-n}\right)}{15x^3y^2\left(0,4ax^2y^2z^2\right)^2}\)
\(D=\frac{\left[3.\frac{6}{11}.8.\left(-2\right)\right]\left(x^8x^3x^{n-7}x^{7-n}\right)\left(y^8y\right)}{15.0,4.\left(x^3x^4\right)\left(y^2y^4\right)z^4a}\)
\(D=\frac{\frac{-188}{11}x^{24}y^9}{6x^7y^6z^4a}\)
\(\Leftrightarrow\left(2x+3;-2y+5\right)\in\left\{\left(1;-7\right);\left(-7;1\right);\left(-1;7\right);\left(7;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(-1;6\right);\left(-5;2\right);\left(-2;-1\right);\left(2;2\right)\right\}\)