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A = (x –y)2+ 4xy
= x2-2xy+y2+4xy
= x2+2xy+y2
=(x+y)2
B = (a + b)2+ (a –b)2
=(a+b+a-b)(a+b-a+b)
=2a.2b
=4ab
\(A=\left(x-y\right)^2+4xy=\left(x+y\right)^2\)
\(B=\left(a+b\right)^2+\left(a-b\right)^2=2a^2+2b^2\)
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\(a,=2xy\left(\dfrac{1}{3}x-y+2\right)\\ b,=\left(2x-3y\right)\left(2x+3y\right)-\left(2x+3y\right)=\left(2x+3y\right)\left(2x-3y-1\right)\)
b: Ta có: \(4x^2-9y^2-2x-3y\)
\(=\left(2x-3y\right)\left(2x+3y\right)-\left(2x+3y\right)\)
\(=\left(2x+3y\right)\left(2x-3y-1\right)\)
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1: Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)
\(=x^3+27-x^3-54\)
=-27
2: Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3\)
\(=2y^3\)
\(1,=x^3+270-x^3-54=-27\\ 2,=8x^3+y^3-8x^3+y^3=2y^3\\ 3,=x^3-3x^2+3x-1-x^3-8+3x^2-48=3x-57\\ 4,=x^3-x-x^3-1=-x-1\\ 5,=8x^3-5\left(8x^3+1\right)=-32x^3-5\\ 6,=27+x^3-27=x^3\\ 7,làm.ở.câu.3\\ 8,=x^3-6x^2+12x-8+6x^2-12x+6-x^3-1+3x\\ =3x-3\)
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\(=\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)\)
\(=\left(x+y\right)^2\cdot\left(x-y\right)^2\)
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Lời giải:
$P=(x+1)^3-(x+1)^3-[(x-1)^2+(x+1)^2]$
$=-[(x-1)^2+(x+1)^2]=-[(x^2-2x+1)+(x^2+2x+1)]=-2(x^2+1)$ phụ thuộc vào giá trị của biến nhé. Bạn xem lại đề.
$Q=(2x)^3-y^3+(2x)^3+y^3-16x^3$
$=8x^3-y^3+8x^3+y^3-16x^3=(8x^3+8x^3-16x^3)+(-y^3+y^3)=0+0=0$ không phụ thuộc vào giá trị của biến (đpcm)
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1b.=2((x+y)+(x+y)(x-y)+(x-y))=2(x2-y2+x+y+x-y)=2(x2-y2+2x)=2x2-2y2+4x
2a.=4xy+4xy+2y=8xy+2y=2y(4x+1)
b.=(3x)2+2.3x.y+y2-(2z)2=(3x+y)2-(2z)2=(3x+y-2z)(3x+y+2z)
c.=x2-x-7x+7=x(x-1)-7(x-1)=(x-1)(x-7)
\(\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)^2\)
\(=\left(2x\right)^2\)
\(=4x^2\)
hk tốt
^^
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\(\left(x+y\right)^2-2\left(x+y\right)+1=\left(x+y-1\right)^2\)
\(4x^2-4x+1-\left(y^2+8y+16\right)=\left(2x-1\right)^2-\left(y+4\right)^2\)
\(=\left(2x-1-y-4\right)\left(2x-1+y+4\right)=\left(2x-y-5\right)\left(2x+y+3\right)\)
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a.
\(1-4x^2=\left(1-2x\right)\left(1+2x\right)\)
b.
\(8-27x^3=\left(2\right)^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
c.
\(27+27x+9x^2+x^3=x^3+3.x^2.3+3.3^2.x+3^3\)
\(=\left(x+3\right)^3\)
d.
\(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
e.
\(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
f.
\(x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
a) \(4x^2+y^2-25+4xy\\ =\left(4x^2+4xy+y^2\right)-25\\ =\left(2x+y\right)^2-5^2\\ =\left(2x+y-5\right)\left(2x+y+5\right)\)
b) \(\left(x-3\right)^2-\left(x+2\right)^2\\ =\left(x-3-x-2\right)\left(x-3+x+2\right)\\ =-5\left(2x-1\right)\)
a. 4x2 + y2 - 25 + 4xy
= (2x)2 + 4xy - 52 - 52
= (2x + 5)2 - 52
= (2x + 5 - 5)(2x + 5 + 5)
= 2x(2x + 10)