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a: \(\left(a^2+2a+3\right)\left(a^2-2a-3\right)\)
\(=\left[a^2+\left(2a+3\right)\right]\left[a^2-\left(2a+3\right)\right]\)
\(=\left(a^2\right)^2-\left(2a+3\right)^2\)
\(=a^4-\left(2a+3\right)^2\)
b: \(\left(-a^2-2a+3\right)^2\)
\(=\left(a^2+2a-3\right)^2\)
\(=a^4+4a^2+9+4a^3-18a-6a^2\)
\(=a^4+4a^3-2a^2-18a+9\)
c: \(\left(x-y-z\right)^2\)
\(=x^2-2x\left(y+z\right)+\left(y+z\right)^2\)
\(=x^2-2xy-2xz+y^2+2yz+z^2\)
d: \(\left(x+y+z\right)\left(x-y-z\right)\)
\(=x^2-\left(y+z\right)^2\)
\(=x^2-y^2-2yz-z^2\)
a) 25x² - 16
= (5x)² - 4²
= (5x - 4)(5x + 4)
b) 16a² - 9b²
= (4a)² - (3b)²
= (4a - 3b)(4a + 3b)
c) 8x³ + 1
= (2x)³ + 1³
= (2x + 1)(4x² - 2x + 1)
d) 125x³ + 27y³
= (5x)³ + (3y)³
= (5x + 3y)(25x² - 15xy + 9y²)
e) 8x³ - 125
= (2x)³ - 5³
= (2x - 5)(4x² + 10x + 25)
g) 27x³ - y³
= (3x)³ - y³
= (3x - y)(9x² + 3xy + y²)
a) \(25x^2-16=\left(5x-4\right)\left(5x+4\right)\)
b) \(16a^2-9b^2=\left(4a-3b\right)\left(4a+3b\right)\)
c) \(8x^3+1=\left(2x+1\right)\left(4x^2-2x+1\right)\)
d) \(125x^3+27y^3=\left(5x+3y\right)\left(25x^2-15xy+9y^2\right)\)
e) \(8x^3-125=\left(2x-5\right)\left(4x^2-10x+25\right)\)
g) \(27x^3-y^3=\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
làm tương tự
Viết các biểu thức sau dưới dạng tích các đa thức?
a)16x^2-9
b)9x^2-25y^2
c)49a^2-4y^4
d)8x^6-125y^6
e)(2x+y)^2-4
f)(x+y+z)^2-(x-y-z)^2
Bài làm
a)16x^2-9
=(4x)^2-3^2
=(4x-3)(4x+3)
b)9x^2-25y^2
=(3x)^2-(5y)^2
=(3x-5y)(3x+5y)
c)49a^2-4y^4
=(7a)^2-(2y^2)^2
=(7a-2y^2)(7a+2y^2)
d)8x^6-125y^6
=(2x^3)^3-(5y^3)^3
=(2x^3-5y^3)(2x^3+5y^3)
e)(2x+y)^2-4
=(2x+y-2)(2x+y+2)
f)(x+y+z)^2-(x-y-z)^2
=(x+y+z-x+y+z)(x+y+z+x-y-z)
=(2x+2y+2z)2x
Bài 8:
Ta có: \(A=-x^2+2x+4\)
\(=-\left(x^2-2x-4\right)\)
\(=-\left(x^2-2x+1-5\right)\)
\(=-\left(x-1\right)^2+5\le5\forall x\)
Dấu '=' xảy ra khi x=1
1:
a: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2zx+2yz\)
b: \(\left(x-y+z\right)^2=x^2+y^2+z^2-2xy+2xz-2yz\)
c: \(\left(x-y-z\right)^2=x^2+y^2+z^2-2xy-2xz+2yz\)
2:
-8x^6-12x^4y-6x^2y^2-y^3
=-(8x^6+12x^4y+6x^2y^2+y^3)
=-(2x^2+y)^3
3:
=(1/3)^2-(2x-y)^2
=(1/3-2x+y)(1/3+2x-y)
a: \(\left(x+y+z\right)^2-\left(y+z\right)^2\)
\(=\left(x+y+z-y-z\right)\left(x+y+z+y+z\right)\)
\(=x\left(x+2y+2z\right)\)
b: \(\left(x-3\right)^2-2\left(x^2-9\right)+\left(x+3\right)^2\)
\(=\left(x-3-x-3\right)^2\)
=36
c: \(\left(a^2-b^2\right)^2-\left(a+b^2\right)^2\)
\(=\left(a^2-b^2-a-b^2\right)\left(a^2-b^2+a+b^2\right)\)
\(=\left(a^2-a-2b^2\right)\left(a^2+a\right)\)
\(=a\cdot\left(a+1\right)\left(a^2-a-2b^2\right)\)