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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
\(a,\left(3x+1\right)^2-2\left(3x+1\right)\left(3x-5\right)+\left(3x-5\right)^2=\left(\left(3x+1\right)-\left(3x-5\right)\right)^2=6^2=36\)
\(b,\left(3x^2-y\right)^2-\left(2x^2+y\right)^2=\left(3x^2-y-2x^2-y\right)\left(3x^2-y+2x^2+y\right)=\left(x^2-2y\right).5x^2\)
a. BT= ((3x+1) - (3x-5))2=62=36
b. BT = (3x2-y-2x2-y). (3x2- y + 2x2+ y) = (x2-2y).5x2
Đặt \(3x-1=y,x+2=z\)
\(\Rightarrow y^2-2yz+z^2=\left(y-z\right)^2\)
\(=\left(3x-1-x-2\right)^2=\left(2x-3\right)^2\)
\(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=x\left[2\left(2x-1\right)^2-3\left(x^2-9\right)-4\left(x+1\right)^2\right]\)
\(=x\left(8x^2-8x+1-3x^2+27-4x^2-8x-4\right)\)
\(=x\left(x^2-16x+28\right)=x\left(x-2\right)\left(x-14\right)\)
\(5\left(2x-1\right)^2+4\left(x-1\right)\left(x+3\right)-2\left(5-3x\right)^2\)
\(=5\left(4x^2-4x+1\right)+4\left(x^2+3x-x-3\right)-2\left(25-30x+9x^2\right)\)
\(=20x^2-20x+5+4x^2+12x-4x-12-50+60x-18x^2\)
\(=6x^2+48x-57\)
\(5\left(2x-1\right)^2+4\left(x-1\right)\left(x+3\right)-2\left(5-3x\right)^2\)
\(=5\left(4x^2-4x+1\right)+4\left(x-1\right)\left(x+3\right)-2\left(5-3x\right)^2\)
\(=5\left(4x^2-4x+1\right)+4\left(x-1\right)\left(x+3\right)-2\left(25-3x+9x^2\right)\)
\(=20x^2-20x+5+4\left(x-1\right)\left(x+3\right)-2\left(25-30x+9x^2\right)\)
\(=20x^2-20x+5+4x^2+8x-12-50+60x-18x^2\)
\(=6x^2+48x-57\)
\(\left(2x+1\right)^2+\left(3x-1\right)^2+2\left(2x+1\right)\left(3x-1\right)\))
= \(\left(2x+1\right)^2+2\left(2x+1\right)\left(3x-1\right)+\left(3x-1\right)^2\)
= \(\left[\left(2x+1\right)+\left(3x-1\right)\right]^2\)
= \(\left[2x+1+3x-1\right]^2\)
=\(\left(5x\right)^2\)= \(25x^2\)