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Đặt \(3x-1=y,x+2=z\)
\(\Rightarrow y^2-2yz+z^2=\left(y-z\right)^2\)
\(=\left(3x-1-x-2\right)^2=\left(2x-3\right)^2\)
\(A=\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2-4a^2b^2\)
\(=\left(a^2+b^2-c^2+a^2-b^2+c^2\right)\left(a^2+b^2-c^2-a^2+b^2-c^2\right)-4a^2b^2\)
\(=2a^2.2b^2-4a^2b^2=0\)
\(C=\left(2-6x\right)^2+\left(2-5x\right)^2+2\left(6x-2\right)\left(2-5x\right)\)
\(=\left[\left(2-6x\right)+\left(2-5x\right)\right]^2\)
\(=\left[4-11x\right]^2\)
\(=16-88x+121x^2\)
chúc bn học tốt
\(\left(5-3x\right)\left(5+3x\right)-\left(x+1\right)^3\)
\(=25-9x^2-x^3-3x^2-3x-1\)
\(=-x^3-12x^2-3x+24\)
\(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
\(=\left[\left(3x+1\right)-\left(3x+5\right)\right]^2\)
\(=\left(3x+1-3x-5\right)^2\)
\(=\left(-4\right)^2=16\)
a: \(\left(3x+4y\right)\left(9x^2-12y+16y^2\right)\)
\(=27x^3-36xy+48xy^2+36x^2y-48y^2+64y^3\)
b: \(\left(x+3\right)^3-\left(3x-1\right)^2\)
\(=x^3+9x^2+27x+27-\left(9x^2-6x+1\right)\)
\(=x^3+9x^2+27x+27-9x^2+6x-1\)
\(=x^3+33x+26\)
`#3107.101107`
`1.`
`a,`
`(3x + 4y)(9x^2 - 12xy + 16y^2)?`
`= (3x)^3 + (4y)^3`
`= 27x^3 + 64y^3`
`b,`
`(x + 3)^3 - (3x - 1)^2`
`= x^3 + 9x^2 + 27x + 27 - (9x^2 - 6x + 1)`
`= x^3 + 9x^2 + 27x + 27 - 9x^2 + 6x - 1`
`= x^3 + 33x + 26`
_____
Sử dụng HĐT:
`A^3 + B^3 = (A + B)(A^2 + AB + B^2)`
`(A + B)^3 = A^3 + 3A^2B + 3AB^2 + B^3`
`(A - B)^2 = A^2 - 2AB + B^2.`
\(=\dfrac{3\left(x+1\right)\left(3x-5\right)}{-\left(3x-5\right)\left(3x+5\right)}=\dfrac{-3\left(x+1\right)}{3x+5}\)
a: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
Ta có:
\(\left(3x^3+3x+1\right)\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)
= \(\left(3x^3+1\right)^2-\left(3x\right)^2-\left(3x^3+1\right)^2\)
= \(9x^2\)
Đặt \(3x^3+1=y\)
\(\Rightarrow\left(y-3x\right)\left(y+3x\right)-y^2\)
\(=y^2-9x^2-y^2=-9x^2\)