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(5x - 2)(x + 1) - 3x(x2 - x - 3) - 2x(x - 5)(x + 4) + 5x(x2 - 7)
= 5x2 + 3x - 2 - 3x3 + 3x2 + 9x - 2x(x2 - x - 20) + 5x3 - 35x
= 2x3 + 8x2 - 23x - 2 - 2x3 + 2x2 + 40x = 10x2 + 17x - 2
5x2 (x - 7) - 4x(x - 2)(x + 3) - (x - 5)(x + 6) + (2x-1)(x + 5)
=5x3-35x2-4x(x2+3x-2x-6)-(x2+6x-5x-30)+2x2+10x-x-5
=5x3-35x2-4x3-12x2+8x2+24x-x2-6x+5x+30+2x2+9x-5
=x3+32x2+32x+25
a) \(A=\left(3x+2\right)^2-9x\left(x+1\right)\)
\(A=9x^2+12x+4-9x^2-9x\)
\(A=3x+4\)
\(B=\left(2x-1\right)^2-2\left(2x-1\right)\left(5x-1\right)+\left(5x-1\right)^2\)
\(B=\left[2x-1-\left(5x-1\right)\right]^2\)
\(B=\left(2x-1-5x+1\right)^2\)
\(B=\left(-3x\right)^2\)
\(B=9x^2\)
(3x - 7)(x + 3) + 5x(x2 - 2x - 4) - (4x - 5)(x-4)-(x + 2)(x + 1)
=3x2+9x-7x-21+5x3-10x2-20x-4x2+16x+5x-20-x2-x-2x-2
=5x3-13x2-43
Bài1: Phân tích các đa thức sau thành nhân tử
a)36-4x2+4xy-y2
\(=6^2-\left(4x^2-4xy+y^2\right)\)
\(=6^2-\left(2x-y\right)^2\)
\(=\left(6+2x-y\right)\left(6-2x+y\right)\)
b)2x4+3x2-5
\(=2x^4-2x^2+5x^2-5\)
\(=2x^2\left(x^2-1\right)+5\left(x^2-1\right)\)
\(=\left(2x^2+5\right)\left(x^2-1\right)\)
\(=\left(2x^2+5\right)\left(x-1\right)\left(x+1\right)\)
B1:a)\(36-4x^2+4xy-y^2=36-\left(4x^2-4xy+y^2\right)=6^2-\left(2x-y\right)^2\)
\(=\left(6-2x+y\right)\left(6+2x-y\right)\)
c)\(a^3-ab^2+a^2+b^2-2ab=a\left(a^2-b^2\right)+\left(a-b\right)^2\)\(=a\left(a-b\right)\left(a+b\right)+\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab+a-b\right)\)
d)\(x^2-\left(a^2+b^2\right)x+a^2b^2=x^2-a^2x-b^2x+a^2b^2\)\(=x\left(x-a^2\right)-b^2\left(x-a^2\right)=\left(x-a^2\right)\left(x-b^2\right)\)
e)\(x\left(x-y\right)+x^2-y^2=x\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)\(=\left(x-y\right)\left(x+x+y\right)=\left(x-y\right)\left(2x+y\right)\)