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1A:
a: \(x^3+2x=x\left(x^2+2\right)\)
b: \(3x-6y=3\left(x-2y\right)\)
c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)
\(=5\left(x+3y\right)\left(1-3x\right)\)
d: \(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+3\right)\)
1A. a. x(x2+2)
b. 3(x-2y)
c. 5(x+3y)(1-3x)
d. (x-y) (3-5x)
1B. a. 2x(2x-3)
b.xy(x2-2xy+5)
c. 2x(x+1)(x+2)
d. 2x(y-1)+2y(y-1)=2(y-1)(x-y)
a) \(12x^3+8x^2-3x-2=4x^2\left(3x+2\right)-\left(3x+2\right)\)
\(=\left(3x+2\right)\left(4x^2-1\right)=\left(3x+2\right)\left(2x-1\right)\left(2x+1\right)\)
b) \(18x^3+27x^2-2x-3=9x^2\left(2x+3\right)-\left(2x+3\right)\)
\(=\left(2x+3\right)\left(9x^2-1\right)=\left(2x+3\right)\left(3x-1\right)\left(3x+1\right)\)
c) \(8x^3+4x^2-34x+15=4x^2\left(2x-3\right)+8x\left(2x-3\right)-5\left(2x-3\right)\)
\(=\left(2x-3\right)\left(4x^2+8x-5\right)=\left(2x-3\right)\left(2x-1\right)\left(2x+5\right)\)
\(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)-3x^2\)
\(=4\left(x+5\right)\left(x+10\right)\left(x+12\right)\left(x+6\right)-3x^2\)
\(=4\left(x^2+17x+60\right)\left(x^2+16x+60\right)-3x^2\)
\(=4\left(x+60\right)^2+132x\left(x+60\right)+1088x^2-3x^2\)
\(=4\left(x+60\right)^2+132x\left(x+60\right)+1085x^2\)
\(=4\left(x+60\right)^2+62x\left(x+60\right)+70x\left(x+60\right)+1085x^2\)
\(=2\left(x+60\right)\left[2\left(x+60\right)+31x\right]+35x\left[2\left(x+60\right)+31x\right]\)
\(=\left(33x+120\right)\left(2x+120+35x\right)\)
\(=3\left(11x+40\right)\left(37x+120\right)\)
Vô đây xem: bài 1:phân tích đa thức thành nhân tửa)7x^3y-14x^2y+7xy^3b)3x^2-3xy-5x+5yc)x^2+7x+12giúp mình với - Hoc24
\(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)+x^2\)
\(=4\left(x^2+5x+10x+50\right)\left(x^2+12x+6x+72\right)+x^2\)
\(=4\left(x+5\right)\left(x+10\right)\left(x+6\right)\left(x+12\right)+x^2\)
\(=4\left(x+6\right)\left(x+10\right)\left(x+5\right)\left(x+12\right)+x^2\)
\(=4\left(x^2+16x+60\right)\left(x^2+17x+60\right)+x^2\)
Đặt \(x^2+16x+60=a\)thay vào ta được :
\(4a\left(a+x\right)+x^2\)
\(=4a^2+4ax+x^2\)
\(=\left(2a+x\right)^2\)
\(=\left(2x^2+32x+120+x\right)^2\)
\(15x^2-34x+15\)
\(=15x^2-25x-9x+15\)
\(=5x\left(3x-5\right)-3\left(3x-5\right)\)
\(=\left(5x-3\right)\left(3x-5\right)\)