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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) \(x^2-81=\left(x-9\right)\left(x+9\right)\)
b) \(4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
c) \(x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
d) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
e) \(6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)
f) \(x^2-4x^2+4y^2+4xy=\left(x^2+4xy+4y^2\right)-4x^2=\left(x+2y\right)^2-4x^2\\ =\left(x+2y+2x\right)\left(x+2y-2x\right)=\left(3x+2y\right)\left(2y-x\right)\)
g) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2a\left(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right)=2a\left(a^2+3b^2\right)\)
h) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)
Bài làm:
a, 1-4x2
=1-(2x)2
=(1-2x).(1+2x)
b, 8-27x3
=23-(3x)3
=(2-3x).(4+6x+9x2)
Các câu còn lại bạn dùng hằng đẳng thức là phân tích được ra thôi
1 - 4x^2
= 1^2 - ( 2x )^2
= ( 1 - 2x ) ( 1 + 2x )
8 - 27x^ 3
= 2^3 - ( 3x )^3
= ( 2 - 3x ) [ 2^2 + 2 * 3x + ( 3x )^2 ]
= ( 2 - 3x ) ( 4 + 6x + 9x^2 )
= ( 2 - 3x ) ( 9x^2 + 6x + 4 )
27 + 27x + 9x^2 + x^3
= x^3 + 9x^2 + 27x + 27
= x^3 + 3x^2 + 6x^2 + 18x + 9x + 27
= x^2 ( x + 3 ) + 6x ( x + 3 ) + 9 ( x + 3 )
= ( x + 3 ) ( x^2 + 6x + 9 )
= ( x + 3 ) ( x + 3 )^2
= ( x + 3 )^3
x^2 + 4x - 5
= x^2 - x + 5x - 5
= x ( x - 1 ) + 5 ( x - 1 )
= ( x + 1 ) ( x - 5 )
\(\left(x-1\right)^2-25\)
\(=x^2-2x+1-25\)
\(=x^2-2x-24\)
\(=x^2-6x+4x-24\)
\(=x.\left(x-6\right)+4.\left(x-6\right)\)
\(=\left(x+4\right).\left(x-6\right)\)
a, \(1-2y+y^2=\left(y+1\right)^2=\left(y+1\right)\left(y+1\right)\)
b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
c, \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
d, \(8-27x^3=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
a) 6x4 - 9x3 = 3x3(2x - 3)
b) 5y10 + 15y6 = 5y6(y4 + 3)
c) x2 - 6xy + 9y2 = x2 - 6xy + (3y)2 = (x - 3y)2
e) x3 - 64 = x3 - 43 = (x - 4)(x2 + 4x + 16)
f) 125x3 + y6 = (5x)3 + (y2)3 = (5x + y2)(25x2 + 5y2 + y4)
g) 0,125(a + 1)3 - 1 = [0,5(a + 1)]3 - 13 = (0,5a + 0,5)3 - 13 = (0,5a + 0,5 - 1)[(0,5a + 0,5)2 + (0,5a + 0,5) + 1) = (0,5a - 0,5)(0,25a^2 + 0,5 a + 0,25 + 0,5a + 0,5 + 1) = (0,5a - 0,5)(0,25a2 + 1,75 + a)
h) 3x2 - 12y2 = 3(x2 - 4y2) = 3[x2 - (2y)2 ] = 3(x - 2y)(x + 2y)
a) 1 - 2y + y2
= (1-y)2
b) ( x + 1 )2 - 25
=( x + 1 )2 - 52
=(x+1+5)(x+1-5)
bài 1: a) \(x^2-3=x^2-\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)\)
b) \(\left(a+b\right)^2-\left(a+b\right)^2=\left(a+b+a+b\right)\left(a+b-a-b\right)=2a+2b=2\left(a+b\right)\)
c) \(x^3-27b^3=\left(x-3b\right)\left(x^2+3xb+b^2\right)\)
a) x2 + xy + y - 1 = (x2 - 1) + (xy + y) = (x - 1)(x + 1) + y(x + 1) = (x + 1)(x + y - 1)
b) 4 - x2 + 2xy - y2 = 4 - (x2 - 2xy + y2) = 4 - (x - y)2 = (x - y + 2)(4 - x + y)
c) 8x2 - 18y2 = 2(4x2 - 9y2) = 2[(2x)2 - (3y)2] = 2(2x - 3y)(2x + 3y)
d) 8x3 - 4x2 - 6xy - 9y2 - 27y3
= (8x3 - 27y3) - (4x2 + 6xy + 9y2)
= (2x - 3y)(4x2 + 6xy + 9y2) - (4x2 + 6xy + 9y2)
= (2x - 3y - 1)(4x2 + 6xy + 9y2)
e) 4x2 - x - 3 = 4x2 - 4x + 3x - 3 = 4x(x - 1) + 3(x - 1) = (x - 1)(4x + 3)
f) 4x2 - 8x + 3 = 4x2 - 2x - 6x + 3 = 2x(2x - 1) - 3(2x - 1) = (2x - 3)(2x - 1)