Question

Rút gọn các biểu thức:

a, P=\(\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)

b, Q=\(\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

Answer 1

a, \(P=\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)

\(=5x-1+2\left(4+5x-20x-25x^2\right)+\left(25x^2+40x+16\right)\)

\(=5x-1+8-30x-50x^2+25x^2+40x+16\)

\(=\left(-50x^2+25x^2\right)+\left(5x-30x+40x\right)+\left(-1+8+16\right)\)

\(=-25x^2+15x+23\)

b, \(Q=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

\(=x^3-3x^2y+3xy^2-y^3+y^3+3y^2x+3yx^2+x^3+y^3-3y^2x+3yx^2-x^3-3x^2y-3xy^2\)

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

\(=x^3+y^3\)

Chúc bạn học tốt!!!