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a) 3x5y3-12x4y4+12x3y5-48x3y3
=(3x5y3-12x4y4)+(12x3y5-48x3y3)
=3x3y3(3x5y3-12x4y4)+(12x3y5-48x3y3)
=(x2-4xy)+(4y2-16)
(Nếu có sai mong bạn thông cảm nhá!!!)
a) 3x^3 - 75x
a^2 - b^2= (a+b)(a-c) trong đó a=x và b=5
3x(x+5)(x-5)
a, ( 2x - 1)^2 - (4x + 2) ^2 = ( 2x - 1 - 4x- 2) ( 2x - 1 + 4x + 2) = (-2x-3)(6x+1) = - (2x+3)(6x+1)
b, 8x^3 + 12x^2y + 6xy^2 + y^3
= (2x)^2 + 3.(2x)^2 . y + 3.2x.y^2 + y^3
= (2x + y)^3
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) Ta có: \(x^3+12x^2+48x+64\)
\(=x^3+3\cdot x^2\cdot4+3\cdot x\cdot4^2+4^3\)
\(=\left(x+4\right)^3\)
b) Ta có: \(x^3-12x^2+48x-64\)
\(=x^3-3\cdot x^2\cdot4+3\cdot x\cdot4^2-4^3\)
\(=\left(x-4\right)^3\)
c) Ta có: \(8x^3+12x^2y+6xy^2+y^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3\)
\(=\left(2x+y\right)^3\)
d)Sửa đề: \(x^3-3x^2+3x-1\)
Ta có: \(x^3-3x^2+3x-1\)
\(=x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3\)
\(=\left(x-1\right)^3\)
e) Ta có: \(8-12x+6x^2-x^3\)
\(=2^3-3\cdot2^2\cdot x+3\cdot2\cdot x^2-x^3\)
\(=\left(2-x\right)^3\)
f) Ta có: \(-27y^3+9y^2-y+\frac{1}{27}\)
\(=\left(\frac{1}{3}\right)^3+3\cdot\left(\frac{1}{3}\right)^2\cdot\left(-3y\right)+3\cdot\frac{1}{3}\cdot\left(-3y\right)^{^2}+\left(-3y\right)^3\)
\(=\left(\frac{1}{3}-3y\right)^3\)
a) Ta có: \(3x^2-6xy+3y^2\)
\(=3\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)^2\)
b) Ta có: \(12x^5y+24x^4y^2+12x^3y^3\)
\(=12x^3y\left(x^2+2xy+y^2\right)\)
\(=12x^3y\left(x+y\right)^2\)
c) Ta có: \(64xy-96x^2y+48x^3y-8x^4y\)
\(=8xy\left(8-12x+6x^2-x^3\right)\)
\(=8xy\left(2-x\right)^3\)
d) Ta có: \(54x^3+16y^3\)
\(=2\left(27x^3+8y^3\right)\)
\(=2\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)\)