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mk ghi đáp án, ko phân tích đc thì IB mk
a) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
b) \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)
c) \(x^6+y^2-2x^3y=\left(x^3-y\right)^2\)
d) \(\left(x+y\right)^3-\left(x-y\right)^3=2y\left(3x^2+y^2\right)\)
e) \(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)
f) \(-a^2-2a-1=-\left(a+1\right)^2\)
g) \(27b^3-8a^3=\left(3b-2a\right)\left(9b^2+6ab+4a^2\right)\)
h) \(x^3+9x^2y+27xy^2+27y^3=\left(x+3y\right)^3\)
i) \(16x^2-9\left(x+y\right)^2=\left(x-3y\right)\left(7x+3y\right)\)
a) ta có : \(x^2+6xy+9y^2=x^2+2.x.3y+\left(3y\right)^2=\left(x+3y\right)^2\)
b) ta có : \(4a^4-4a^2b^2+b^4=\left(2a^2\right)^2-2.2a^2.b^2+\left(b^2\right)^2=\left(2a^2-b^2\right)^2\)
c) ta có : \(x^6+y^2-2x^3y=\left(x^3\right)^2-2.x^3.y+y^2=\left(x^3-y^2\right)^2\)
d) ta có : \(\left(x+y\right)^3-\left(x-y\right)^3=\left(x+y-x+y\right)\left(\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right)\)
\(=2y\left(x^2+y^2+2xy+2x^2-2y^2+x^2+y^2-2xy\right)\)
\(=2y\left(4x^2\right)=8x^2y\)
e) ta có : \(25x^4-10x^2y^2+y^4=\left(5x^2\right)^2-2.5x^2.y^2+\left(y^2\right)^2=\left(5x^2-y^2\right)^2\)
f) ta có : \(-a^2-2a-1=-\left(a^2+2a+1\right)=-\left(a+1\right)^2\)
g) ta có : \(27b^3-8a^3=\left(3b\right)^3-\left(2a\right)^3=\left(3b-2a\right)\left(9b^2+6ab+4a^2\right)\)
i) ta có : \(16x^2-9\left(x+y\right)^2=\left(4x\right)^2-\left(3\left(x+y\right)\right)^2\)
\(=\left(4x-3x-3y\right)\left(4x+3x+3y\right)=\left(x-3y\right)\left(7x+3y\right)\)
a) \(\left(2x^3-y^2\right)^3\)
\(=\left(2x^3\right)^3-3\cdot\left(2x^3\right)^2\cdot y^2+3\cdot2x^3\cdot\left(y^2\right)^{^2}-\left(y^2\right)^3\)
\(=8x^9-3\cdot4x^6y^2+3\cdot2x^3y^4-y^6\)
\(=8x^9-12x^6y^2+6x^3y^4-y^6\)
b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)
\(=x^3-\left(3y\right)^3\)
\(=x^3-27y^3\)
c) \(\left(x+2y+z\right)\left(x+2y-z\right)\)
\(=\left(x+2y\right)^2-z^2\)
\(=x^2+4xy+4y^2-z^2\)
d) \(\left(2x^3y-0,5x^2\right)^3\)
\(=\left(2x^3y-\dfrac{1}{2}x^2\right)^3\)
\(=8x^9y^3-6x^8y^2+\dfrac{3}{2}x^7y-\dfrac{1}{8}x^6\)
e) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)
\(=\left(x^2-3\right)\left(4x^2+9\right)\)
\(=4x^4+9x^2-12x^2-27\)
\(=4x^4-3x^2-27\)
f) \(\left(2x-1\right)\left(4x^2+2x+1\right)\)
\(=\left(2x\right)^3-1^3\)
\(=8x^3-1\)
\(a,\left(2x^3-y^2\right)^3=8x^9-12x^6y^2+6x^3y^4-y^6\)\(b,\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)
\(c,\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-z^2=x^2+4xy+4y^2-z^2\)\(d,\left(2x^3y-0,5x^2\right)^3=8x^9y^3-6x^4y^2x^2+3x^3yx^4-0,125x^6=8x^9y^3-6x^6y^2+3x^7y-0,125x^6\)
a: \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
b: \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)
\(x^6-2x^3y+y^2=\left(x^3-y\right)^2\)
b: \(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\left(3x^2+y^2\right)\)
\(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)
\(-a^2-2a-1=-\left(a+1\right)^2\)
a) (x - 1)2 = x2 - 2x + 1
b) ( x + 2 )2 = x2 + 4x + 4
c) (y + 2a )2 = y2 + 4ya + 4a2
e) (2x - y)3 = ( 2x )3 - 3.(2x)2.y + 3.2x.y2 - y3 = 8x3 - 12x2y + 6xy2 - y3
g) (3a+6)3 = (3a)3 + 3.(3a)2.6 + 3.3a.62 + 63 = 27a3 + 162a2 + 324a + 216