PT da thuc thanh nhan tu:
a(a+2b)3 - b(2a+b)3
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Phan tich da thuc thanh nhan tu
a(a+2b)^3-b(2a+b)^3
=a(a+2b)^3-[-b(a+2b)^3]
=(a+2b)^3(a+b)
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PT da thuc thanh nhan tu:
a(a+2b)3 - b(2a+b)3
= a( a3 + 6a2b + 12ab2 + 8b3 ) - b( 8a3 + 12a2b + 6ab2 + b3)
= a4 + 6a3b +12a2b2 + 8ab3 - 8a3b - 12a2b2 - 6ab3 - b4
= a4 - 2a3b + 2ab3 -b4
= (a2 + b2) (a2 - b2) - 2ab2 (a - b)
= (a2 + b2) (a + b) ( a - b )- 2ab ( a - b )
= ( a - b) ( (a2 + b2)( a + b )- 2ab)
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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 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:(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 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 : \(a^6+a^4+a^2b^2+b^4-b^6\)
\(a^6+a^4+a^2b^2+b^4-b^6\)
\(=(a^2)^3-(b^2)^3+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2)(a^4+a^2b^2+b^4)+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2+1)(a^4+a^2b^2+b^4)\)
\(=(a^4+2a^2b^2+b^4-a^2b^2)(a^2-b^2+1)\)
\(=(a^2+ab+b^2)(a^2-ab+b^2)(a^2-b^2+1)\)
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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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phan tich da thuc thanh nhan tu
4a^2b^2-(a^2+b^2-c^2)^2
a^3(b-c)+ b^3(c-a)+c^3(a-b) phan tich da thuc thanh nhan tu