Question

1, Tính:

a,( \(\dfrac{4}{3}\)\(x^3\) + \(\dfrac{2}{3}\)\(x^2\) - \(\dfrac{1}{3}\)) . ( -3\(x^2\) )

b, ( x - 3y ) ( 3\(x^2\) + 4\(y^2\) + 5xy )

c, ( x + 8 )\(^2\) - 2 ( x + 8 ) ( x - 2 ) + ( x - 2 )\(^2\)

d, x ( x - 4 ) ( x + 4 ) - ( x\(^2\) + 1 ) ( x\(^2\) - 1 )

Answer 1

a: \(-3x^2\cdot\left(\dfrac{4}{3}x^2+\dfrac{2}{3}x^2-\dfrac{1}{3}\right)\)

\(=-4x^4-2x^4+x^2\)

b: \(\left(x-3y\right)\left(3x^2+5xy+4y^2\right)\)

\(=3x^3+5x^2y+4xy^2-9x^2y-15xy^2-12y^3\)

\(=3x^3-4x^2y-11xy^2-12y^3\)

c: \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)

\(=\left(x+8-x+2\right)^2\)

\(=10^2=100\)

d: \(x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x\left(x^2-16\right)-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x^3-16x-x^4+1\)