Question

Cho x + 2y = -5. Tính giá trị biểu thức:

a/ \(x\left(x-3\right)+2y\left(2y-3\right)-4xy+19\)

b/\(x^2\left(x+1\right)+4y^2\left(2y+1\right)+2xy\left(3x+6y+2\right)+70\)

Answer 1

Sửa đề: \(x\left(x-3\right)+2y\left(2y-3\right)+4xy+19\)

a: \(x\left(x-3\right)+2y\left(2y-3\right)+4xy+19\)

\(=x^2-3x+4y^2-6y+4xy+19\)

\(=\left(x^2+4xy+4y^2\right)-3\left(x+2y\right)+19\)

\(=\left(x+2y\right)^2-3\left(x+2y\right)+19\)

\(=\left(-5\right)^2-3\cdot\left(-5\right)+19\)

=25+15+19=59

b: \(=x^3+x^2+8y^3+4y^2+2xy\left[3\left(x+2y\right)+2\right]+70\)

\(=x^3+8y^3+x^2+4y^2+2xy\cdot\left[3\cdot\left(-5\right)+2\right]+70\)

\(=\left(x+2y\right)^3-3\cdot x\cdot2y\left(x+2y\right)+\left(x+2y\right)^2-4xy+2xy\cdot\left(-13\right)+70\)

\(=\left(-5\right)^3+\left(-5\right)^2-6xy\cdot\left(-5\right)-4xy-26xy\)+70

\(=-125+25+70=-30\)