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a) \(x^2+4y^2+4xy\)
\(=x^2+2.x.2y+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
b) \(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x+y-x+y\right)\left(x+y+x-y\right)\)
\(=2y.2x\)
\(=4xy\)
c) \(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1-x-1\right)\left(3x+1+x-1\right)\)
a) \(x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)\)
a: \(A=x^2+y^2=\left(x+y\right)^2-2xy=15^2-2\cdot50=115\)
c: \(x-y=\sqrt{\left(x+y\right)^2-4xy}=\sqrt{15^2-4\cdot50}=5\)
\(C=x^2-y^2=\left(x+y\right)\left(x-y\right)=15\cdot5=75\)
a: \(A=x^2+y^2=\left(x+y\right)^2-2xy=15^2-2\cdot50=125\)
b:\(B=x^4+y^4\)
\(=\left(x^2+y^2\right)^2-2x^2y^2\)
\(=125^2-2\cdot2500\)
=10625
c: \(x-y=\sqrt{\left(x+y\right)^2-4xy}=\sqrt{15^2-4\cdot50}=5\)
\(C=x^2-y^2=\left(x-y\right)\left(x+y\right)=15\cdot5=75\)
a: \(x^2+y^2=\left(x-y\right)^2+2xy=15^2+2\cdot50=325\)
b: \(x+y=\sqrt{\left(x-y\right)^2+4xy}=\sqrt{15^2+4\cdot50}=5\sqrt{17}\)
\(x^2-y^2=\left(x-y\right)\left(x+y\right)=5\sqrt{17}\cdot15=75\sqrt{17}\)
\(x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=75\sqrt{17}\cdot325=24375\sqrt{17}\)
chắc đề cho x,y chứ x+y=6,x-y=4,xy=5
(làm ra bạn tự thay số vào tính)
a,\(=>A=\left(x+y\right)^2-2xy=.....\)
b,\(=>B=\left(x+y\right)^3-3xy\left(x+y\right)+xy=....\)
c,\(=>C=\left(x-y\right)\left(x+y\right)=....\)
d,\(=>D=\dfrac{x+y}{xy}=.....\)
e,\(=>E=\dfrac{x^2+y^2}{xy}=\dfrac{\left(x+y\right)^2-2xy}{xy}=...\)
1) \(x-y=3\\ \Rightarrow\left(x-y\right)^2=3^2\\ \Rightarrow x^2-2xy+y^2=9\\ \Rightarrow\left(x^2+y^2\right)-2xy=9\\ \Rightarrow x^2+y^2=9+2xy\)
\(\Rightarrow x^2+y^2=9-4\)(vì xy=-2)
\(\Rightarrow x^2+y^2=5\)
Ta có: \(x^6-2x^4+x^3+x^2-x\)
\(=x^6-x^4-x^4+x^2+x^3-x\)
\(=x^4\left(x^2-1\right)-x^2\left(x^2-1\right)+\left(x^3-x\right)\)
\(=x^2\left(x^2-1\right)^2+8\)
\(=\left(x^3-x\right)^2+8\)
=72
Bài 4
c) x(x - 2) + (x - 2)²
= (x - 2)(x + x - 2)
= (x - 2)(2x - 2)
= 2(x - 2)(x - 1)
d) 2x(x - y)² - 5(y - x)
= 2x(x - y)² + 5(x - y)
= (x - y)(2x + 5)
Bài 5
a) x² - 6x - 2xy + 12y
= (x² - 6x) - (2xy - 12y)
= x(x - 6) - y(x - 6)
= (x - 6)(x - y)
b) 10ax - 5ay - 2x + y
= (10ax - 5ay) - (2x - y)
= 5a(2x - y) - (2x - y)
= (2x - y)(5a - 1)
c) x⁴ + x³y - x - y
= (x⁴ + x³y) - (x + y)
= x³(x + y) - (x + y)
= (x + y)(x³ - 1)
= (x + y)(x - 1)(x² + x + 1)
d) x³ + 2x² - 4x - 8
= (x³ + 2x²) - (4x + 8)
= x²(x + 2) - 4(x + 2)
= (x + 2)(x² - 4)
= (x + 2)(x + 2)(x - 2)
= (x + 2)²(x - 2)
e) xy - 5x - y² + 5y
= (xy - 5x) - (y² - 5y)
= x(y - 5) - y(y - 5)
= (y - 5)(x - y)
f) ax - bx - 2cx - 2a + 2b + 4c
= (ax - bx - 2cx) - (2a - 2b - 4c)
= x(a - b - 2c) - 2(a - b - 2c)
= (a - b - 2c)(x - 2)
g) 5x²y + 5xy² - b²x - b²y
= (5x²y + 5xy²) - (b²x + b²y)
= 5xy(x + y) - b²(x + y)
= (x + y)(5xy - b²)
h) 4x³ - 4x² - 9x + 9
= (4x³ - 4x²) - (9x - 9)
= 4x²(x - 1) - 9(x - 1)
= (x - 1)(4x² - 9)
= (x - 1)(2x - 3)(2x + 3)
Tính a, x2+y2
= x2 + 2xy + y2 - 2xy
= ( x + y )2 - 2xy
Thay x + y = 3 và x.y = 2
=> 32 - 2 . 2
= 9 - 4
= 5
Mấy cái sau cũng tách ra nhá