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Phân tích đa thức sau thành nhân tử
a) 8x3 - 27=(2x-3)(4x2+6x+9)
b) 3x ( x - 7) - 5y ( y- x) xem lại đề hộ mk câu này vs nhá
c) 5xy2 - 10xyz + 5xz2=5x(y2-2yz+z2)=5x(y-z)2
1) \(\left(x^2+8x+7\right).\left(x+3\right).\left(x+5\right)+15\)
\(=\left(x^2+8x+7\right).\left(x^2+5x+3x+15\right)+15\)
\(=\left(x^2+8x+7\right).\left(x^2+8x+15\right)+15\)
Ta đặt: \(x^2+8x+7=n\)
\(=n.\left(n+8\right)+15\)
\(=n^2+8n+15\)
\(=n^2+3n+5n+15\)
\(=\left(n^2+3n\right)+\left(5n+15\right)\)
\(=n.\left(n+3\right)+5.\left(n+3\right)\)
\(=\left(n+3\right).\left(n+5\right)\)
\(=\left(x^2+8x+7+3\right).\left(x^2+8x+7+5\right)\)
\(=\left(x^2+8x+10\right).\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right).\left(x^2+2x+6x+12\right)\)
\(=\left(x^2+8x+10\right).[x.\left(x+2\right)+6.\left(x+2\right)]\)
\(=\left(x^2+8x+10\right).\left(x+2\right).\left(x+6\right)\)
2) \(x^2-2xy+3x-3y-10+y^2\)
\(=\left(x-y\right)^2+3.\left(x-y\right)-10\)
Ta đặt: \(x-y=n\)
\(=n^2+3n-10\)
\(=n^2-2n+5n-10\)
\(=\left(n^2-2n\right)+\left(5n-10\right)\)
\(=n.\left(n-2\right)+5.\left(n-2\right)\)
\(=\left(n-2\right).\left(n+5\right)\)
\(=\left(x-y-2\right).\left(x-y+5\right)\)
x7+x6+x5-x6-x5-x4+x5+x4+x3-x3-x2-x1+x2+x1+1
= x5(x2+x+1) - x4(x2+x+1)+x3(x2+x+1)-x(x2+x+1) +(x2+x+1)
=(x2+x+1)( x5-x4+x3-x+1)
────(♥)(♥)(♥)────(♥)(♥)(♥) __ ɪƒ ƴσυ’ʀє αʟσηє,
──(♥)██████(♥)(♥)██████(♥) ɪ’ʟʟ ɓє ƴσυʀ ѕɧα∂σѡ.
─(♥)████████(♥)████████(♥) ɪƒ ƴσυ ѡαηт тσ cʀƴ,
─(♥)██████████████████(♥) ɪ’ʟʟ ɓє ƴσυʀ ѕɧσυʟ∂єʀ.
──(♥)████████████████(♥) ɪƒ ƴσυ ѡαηт α ɧυɢ,
────(♥)████████████(♥) __ ɪ’ʟʟ ɓє ƴσυʀ ρɪʟʟσѡ.
──────(♥)████████(♥) ɪƒ ƴσυ ηєє∂ тσ ɓє ɧαρρƴ,
────────(♥)████(♥) __ ɪ’ʟʟ ɓє ƴσυʀ ѕɱɪʟє.
─────────(♥)██(♥) ɓυт αηƴтɪɱє ƴσυ ηєє∂ α ƒʀɪєη∂,
───────────(♥) __ ɪ’ʟʟ ʝυѕт ɓє ɱє.
x7y+x5y+x3y=x3y.(x4+x2+1)
=x3y.(x4+2x2+1-x2)
=x3y.[(x2+1)2-x2]
=x3y.(x2-x+1)(x2+x+1)
\(9\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(3^2\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(\left[3\left(x-5\right)\right]^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15\right)^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15-x-7\right)\left(3x-15+x+7\right)\)
\(=\)\(\left(2x-22\right)\left(4x-8\right)\)
\(=\)\(2\left(x-11\right).4\left(x-2\right)\)
\(=\)\(8\left(x-11\right)\left(x-2\right)\)
Chúc bạn học tốt ~
a) \(x^5+x-1\)
\(=x^5+x^4+x^3+x^2-x^4-x^3-x^2+x-1\)
\(=\left(x^5-x^4+x^3\right)+\left(x^4-x^3+x^2\right)-\left(x^2-x+1\right)\)
\(=x^3\left(x^2-x+1\right)+x^2\left(x^2-x+1\right)-\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^3+x^2-1\right)\)(còn 1 cách nữa là thêm bớt \(x^2\)vào bạn nhé!)
b) \(x^7+x^2+1\)
\(=x^7-x+x^2+x+1\)
\(=x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3+1\right)\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3+1\right)\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x^3+1\right)\left(x-1\right)+1\right]\)
\(=\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)
(Chúc bạn học tốt và nhớ tíck cho mình với nhé!)