Phan tich da thuc thanh nhan tu
a(a+2b)^3-b(2a+b)^3
Những câu hỏi liên quan
1 phan tich da thuc thanh nhan tu
a) 4x^2 - 49
b) a^2 -2a -b^2 -2b
a/ \(4x^2-49=\left(2x\right)^2-7^2=\left(2x-7\right)\left(2x+7\right)\)
b/ \(a^2-2a-b^2-2b=\left(a^2-2a+1\right)-\left(b^2+2b+1\right)=\left(a-1\right)^2-\left(b+1\right)^2\)
\(=\left(a-1-b-1\right)\left(a-1+b+1\right)=\left(a-b-2\right)\left(a+b\right)\)
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phan tich da thuc:(a^2+b^2-c^2)^2-4a^2b^2 thanh nhan tu
\(\left(a^2+b^2-c^2\right)^2-4a^2b^2\)
\(=\left(a^2+b^2-c^2\right)^2-\left(2ab\right)^2\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[\left(a-b\right)^2+c^2\right]\)
=(a+b+c)(a+b-c)(a-b+c)(a-b-c)
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Phan tich da thuc sau thanh nhan tu:
a) \(a\left(b+c\right)^2+b\left(c+a\right)^2+c\left(a+b\right)^2\)
b)\(a^4+b^4+c^4-2a^2b^2-2a^2c^2-2c^2b^2\)
phan tich da thuc thanh nhan tu
4a^2b^2-(a^2+b^2-c^2)^2
phan tich da thuc thanh nhan tu : \(a^6+a^4+a^2b^2+b^4-b^6\)
\(a^6+a^4+a^2b^2+b^4-b^6\)
\(=(a^2)^3-(b^2)^3+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2)(a^4+a^2b^2+b^4)+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2+1)(a^4+a^2b^2+b^4)\)
\(=(a^4+2a^2b^2+b^4-a^2b^2)(a^2-b^2+1)\)
\(=(a^2+ab+b^2)(a^2-ab+b^2)(a^2-b^2+1)\)
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\(a^6+a^2b^2+a^4+b^2-b^6\)
\(=a^4\left(a^2+b^2\right)+a^2\left(a^2+b^2\right)-b^6\)
\(=\left(a^2+b^2\right)+\left(a^4+a^2\right)-b^6\)
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a^3(b-c)+ b^3(c-a)+c^3(a-b) phan tich da thuc thanh nhan tu
phan tich cac da thuc sau thanh nhan tu
a, (x-y)3 - (z-y)3 - (x-z)3
b, (2016x-2015)3 + (2014-2013x)3 + ( 1-3x)3
c, (2a+b+c)3 - (a-b+2c)3 - (a+2b-c)3
phan tich da thuc thanh nhan tu a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)
\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)
\(=a\left(b^3-c^3\right)-b\left(a^3-c^3\right)+c\left(a^3-b^3\right)\)
\(=a\left(b^3-c^3\right)-b\left[\left(a^3-b^3\right)+\left(b^3-c^3\right)\right]+c\left(a^3-b^3\right)\)
\(=a\left(b^3-c^3\right)-b\left(b^3-c^3\right)-b\left(a^3-b^3\right)+c\left(a^3-b^3\right)\)
\(=\left(b^3-c^3\right)\left(a-b\right)-\left(a^3-b^3\right)\left(b-c\right)\)
\(=\left(b-c\right)\left(b^2+bc+c^2\right)\left(a-b\right)-\left(a-b\right)\left(a^2+ab+b^2\right)\left(b-c\right)\)
\(=\left(a-b\right)\left(b-c\right)\left[\left(b^2+bc+c^2\right)-\left(a^2+ab+b^2\right)\right]\)
\(=\left(a-b\right)\left(b-c\right)\left(bc+c^2-a^2-ab\right)\)
\(=\left(a-b\right)\left(b-c\right)\left[b\left(c-a\right)+\left(c-a\right)\left(c+a\right)\right]\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\left(a+b+c\right)\)
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a(b3−c3)+b(c3−a3)+c(a3−b3)
=a(b3−c3)−b(a3−c3)+c(a3−b3)
=a(b3−c3)−b[(a3−b3)+(b3−c3)]+c(a3−b3)
=a(b3−c3)−b(b3−c3)−b(a3−b3)+c(a3−b3)
=(b3−c3)(a−b)−(a3−b3)(b−c)
=(b−c)(b2+bc+c2)(a−b)−(a−b)(a2+ab+b2)(b−c)
=(a−b)(b−c)[(b2+bc+c2)−(a2+ab+b2)]
=(a−b)(b−c)(bc+c2−a2−ab)
=(a−b)(b−c)[b(c−a)+(c−a)(c+a)]
=(a−b)(b−c)(c−a)(a+b+c)
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phan tich da thuc thanh nhan tu a(b^3-c^3)+b(c^3-a^3)+c(a^3-b^3)