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a: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
\(\left(x^2-1\right)\left(x+2\right)-\left(x-4\right)\left(x^2+4x+16\right)\)
\(=x^3+2x^2-x-2-\left(x^3-4^3\right)\)
\(=x^3+2x^2-x-2-x^3+64\)
\(=2x^2-x+62\)
\(2x\left(3x-2\right)^2\)
\(=2x\left(9x^2-12x+4\right)\)
\(=18x^3-24x^2+8x\)
\(\left(x-3\right)\left(x^2-3x+9\right)\)
\(=x^3-3x^2+9x-3x^2+9x-27\)
\(=x^3-3x^2+18x-27\)
\(\left(x^2-1\right)\left(x+2\right)-\left(x-4\right)\left(x^2+4x+16\right)\)
\(=\left(x^2-1^2\right)\left(x+2\right)-x^3-4^3\)
\(=\left(x+1\right)\left(x-1\right)\left(x+2\right)-x^3-64\)
a) (x+2)(x−2)−(x−3)(x+1)
=x2−22−(x2+x−3x−3)
=x2−4−x2−x+3x+3
=2x−12x−1
b) (2x+1)2+(3x−1)2+2(2x+1)(3x−1)(
=(2x+1)2+2.(2x+1)(3x−1)+(3x−1)2
=[(2x+1)+(3x−1)]2
= (2x+1+3x−1)2
=(5x)2=25x2
Rút gọn biểu thức:
\(\left(x+3\right)^2+\left(2x+1\right)\left(3x-5\right)-2x\left(3-x\right)+4x+25\)
\(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=x\left[2\left(2x-1\right)^2-3\left(x^2-9\right)-4\left(x+1\right)^2\right]\)
\(=x\left(8x^2-8x+1-3x^2+27-4x^2-8x-4\right)\)
\(=x\left(x^2-16x+28\right)=x\left(x-2\right)\left(x-14\right)\)
a) (x + 3)(x2 – 3x + 9) – (54 + x3) = (x + 3)(x2 – 3x + 32 ) - (54 + x3)
= x3 + 33 - (54 + x3)
= x3 + 27 - 54 - x3
= -27
b) (2x + y)(4x2 – 2xy + y2) – (2x – y)(4x2 + 2xy + y2)
= (2x + y)[(2x)2 – 2 . x . y + y2] – (2x – y)(2x)2 + 2 . x . y + y2]
= [(2x)3 + y3]- [(2x)3 - y3]
= (2x)3 + y3- (2x)3 + y3= 2y3
Bài giải:
a) (x + 3)(x2 – 3x + 9) – (54 + x3) = (x + 3)(x2 – 3x + 32 ) - (54 + x3)
= x3 + 33 - (54 + x3)
= x3 + 27 - 54 - x3
= -27
b) (2x + y)(4x2 – 2xy + y2) – (2x – y)(4x2 + 2xy + y2)
= (2x + y)[(2x)2 – 2 . x . y + y2] – (2x – y)(2x)2 + 2 . x . y + y2]
= [(2x)3 + y3]- [(2x)3 - y3]
= (2x)3 + y3- (2x)3 + y3= 2y3
\(=x^3-27-4x^2+4x-1=x^3-4x^2+4x-28\)
thank you!