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a) x^2+ 2x + 1
= x^2+2.x.1+1^2
=(x+1)^2
b) x^2 + 6x + 9
= x^2+2.x.3+3^2
=(x+3)^2
c) x^2 - 6x +9
=x^2-2.x.3+3^2
=(x-3)^2
d) x^2 - 2x + 1
=x^2-2.x.1+1^2
=(x-1)^2
e) 4x^2 + 4xy + y^2
=(2x)^2+2.2x.y+y^2
=(2x+y)^2
phân tích các đa thức sau thành nhân tử
a) 4x^2 - 4xy + 4y^2
\(=\) \(\left(2x\right)^2-4xy+\left(2y\right)^2\)
\(=\left(2x-2y\right)^2\)
b) x^2 - 4xy +4y^2
\(=x^2-4xy+\left(2y\right)^2\)
\(=\left(x-2y\right)^2\)
c) x^2 + 10x + 25
\(=x^2+2.x.5+5^2\)
\(=\left(x+5\right)^2\)
d)x^2 - 10x + 25
\(=x^2-2.x.5+5^2\)
\(=\left(x-5\right)^2\)
e) 81 - (x+1)^2
\(=9^2-\left(x+1\right)^2\)
\(=\left(9-x-1\right)\left(9+x+1\right)\)
f) 16x^2 - 64 (y + 1)^2
\(=16x^2-8^2\left(y+1\right)^2\)
\(=16x^2-\left(8y+8\right)^2\)
\(=\left(16-8y-8\right)\left(16+8y+8\right)\)
p/s: ko chắc câu cuối đâu :v
a)x3-6x2+9x=x(x2-6x+9)=x(x-3)2
b)x2-2x-4y2-4y=(x2-2x+1)-(4y2+4y+1)=(x-1)2-(2y+1)2=(x-1-2y-1)(x-1+2y+1)=(x-2y-2)(x+2y)
c)x2-x+xy-y=x(x-1)+y(x-1)=(x-1)(x+y)
d)3x2-6xy-75+3y2=3[(x2-2xy+y2)-25]=3[(x-y)2-52]=3(x-y-5)(x-y+5)
e)2x2-5x-7=(2x2+2x)-(7x+7)=2x(x+1)-7(x+1)=(x+1)(2x-7)
f)x4+36=x4+12x2+36-12x2=(x2+6)2-12x2=(x2-\(\sqrt{12}x\)+6)(x2+\(\sqrt{12}x\)+6)
h)x4+4y4=x4+4x2y2+4y2-4x2y2=(x2+2y2)-4x2y2=(x2+2y2-2xy)(x2+2y2+2xy)
a) \(4x^2-4xy+y^2-9\)
\(=\left(2x-y\right)^2-3^2\)
\(=\left(2x-y+3\right)\left(2x-y-3\right)\)
b) \(x^2-36+4xy+4y^2\)
\(=\left(4y^2+4xy+x^2\right)-36\)
\(=\left(2y+x\right)^2-6^2\)
\(=\left(2y+x+6\right)\left(2y+x-6\right)\)
c) \(9x^2-12xy-25+4y^2\)
\(=\left(9x^2-12xy+4y^2\right)-25\)
\(=\left(3x-2y\right)^2-5^2\)
\(=\left(3x-2y+5\right)\left(3x-2y-5\right)\)
d) \(25x^2+10x-4y^2+1\)
\(=\left(25x^2+10x+1\right)-4y^2\)
\(=\left(5x+1\right)^2-\left(2y\right)^2\)
\(=\left(5x+2y+1\right)\left(5x-2y+1\right)\)
a) = (x + 3)2 - y2 = (x + 3 - y)(x + 3 + y)
b) = x2(x - 3) -4(x - 3) = (x - 3)(x2 - 4) = (x - 3)(x - 2)(x + 2)
c) = 3x(x - y) - 5(x - y) = (x - y)(3x - y)
d) Nhầm đề. tui sửa lại x3 + y3 + 2x2 - 2xy + 2y2
= x3 + y3 + 2(x2 - xy + y2) = (x + y)(x2 - xy + y2) + 2(x2 - xy + y2) = (x2 - xy + y2)(x + y + 2)
e) = x4 - x3 - x3 + x2 - x2 + x + x - 1 = x3(x - 1) - x2(x - 1) - x(x - 1) + x - 1 = (x - 1)(x3 - x2 - x + 1) = (x - 1)(x - 1)(x2 - 1) = (x - 1)3(x + 1)
f) = x3 - 3x2 - x2 + 3x + 9x - 27 = x2(x - 3) - x(x - 3) + 9(x - 3) = (x-3)(x2 - x + 9)
g) chắc là 3xyz
= x2y + xy2 + y2z + yz2 + x2z + xz2 + 3xyz = x2y + xy2 + xyz + y2z + yz2 + xyz + x2z + xz2 + xyz = (x + y + z)(xy + yz + xz)
h) = 23 -(3x)3 = (2 - 3x)(4 + 6x + 9x2)
i) = (x + y - x + y)(x + y + x - y) = 2y*2x = 4xy
k) = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy +y2)(x + y)(x2 - xy +y2).
a) x^2 + 2x + 1
=\(x^2+2.x.1+1^2\)
\(=\left(x+1\right)^2\)
b) x^2 + 6x + 9
=\(x^2+2.x.3+3^2\)
\(=\left(x+3\right)^2\)
c) x^2 - 6x + 9
\(=x^2-2.x.3+3^2\)
=\(\left(x-3\right)^2\)
d) x^2 - 2x + 1
\(=x^2-2.x.1+1^2\)
\(=\left(x-1\right)^2\)
e ) 4x^2 + 4xy +y^2
\(=\left(2x\right)^2+2.2x.y+y^2\)
\(=\left(2x+y\right)^2\)
f) x^2 + 4xy + 4y^2
\(=x^2+2.x.2y+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
phân tích các đa thức sau thành nhân tử
a) x^2 + 2x + 1
\(=\left(x+1\right)^2\)
b) x^2 + 6x + 9
\(=\left(x+3\right)^2\)
c) x^2 - 6x + 9
\(=\left(x-3\right)^2\)
d) x^2 - 2x + 1
\(=\left(x-1\right)^2\)
e ) 4x^2 + 4xy +y^2
\(=\left(2x\right)^2+4xy+y^2\)
\(=\left(2x+y\right)^2\)
f) x^2 + 4xy + 4y^2
\(=x^2+4xy+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
p/s: --.--