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1) \(x^2+2xy+y^2-x-y-12\)
= \(\left(x+y\right)^2-\left(x+y\right)-12\)
Đặt \(x+y=z\) (đặt ẩn phụ)
\(\Rightarrow z^2-z-12\)
\(=z^2+3z-4z-12\)
\(=z\left(z+3\right)-4\left(z+3\right)\)
\(=\left(z+3\right)\left(z-4\right)\)
Khi đó: \(\left(x+y+3\right)\left(x+y-4\right)\)
#HuyenAnh
\(b,a^6+a^4+a^2b^2+b^4-b^6=\left(a^6-b^6\right)+\left(a^4+a^2b^2+b^4\right)=\left(a^2-b^2\right)^3+\left(a+b\right)^2\)
bạn tự làm ra lun vs lại câu c/ cũng khá dễ đấy ngày mai nhớ k nha\(a,3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)=3\left(x^2+x+1\right)^2-\left(x^2+x+1\right)^2=\left(x^2+x+1\right)^2\left(3-1\right)=\left(x^4+x^2+1\right)4\)
a/ \(E=a^6+a^4+a^2b^2+b^4-b^6\)
\(E=\left[\left(a^2\right)^2+2a^2b^2+\left(b^2\right)^2\right]+\left(a^6-b^6\right)-a^2b^2\)
\(E=\left[\left(a^2+b^2\right)^2-\left(ab\right)^2\right]+\left(a^3-b^3\right)\left(a^3+b^3\right)\)
\(E=\left(a^2-ab+b^2\right)\left(a^2+ab+b^2\right)+\left(a-b\right)\left(a^2+ab+b^2\right)\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(E=\left(a^2-ab+b^2\right)\left(a^2+ab+b^2\right)\left[1+\left(a-b\right)\left(a+b\right)\right]\)
\(E=\left(a^2-ab+b^2\right)\left(a^2+ab+b^2\right)\left(1+a^2-b^2\right)\)
\(a^6+a^4+a^2b^2+b^4-b^6\)
\(a^2\left(a^4+a^2b^2+b^4\right)-b^2\left(a^4+a^2b^2+b^4\right)+\left(a^4+a^2b^2+b^4\right)\)
\(=\left(a^4+a^2b^2+b^4\right)\left(a^2-b^2+1\right)\)
\(=\left(a^2+b^2+ab\right)\left(a^2+b^2-ab\right)\left(a^2-b^2+1\right)\)
Mấy câu dễ mình làm trước nhé. Mấy câu khó hơn mình trình bày sau :)
1) 2x2 - 5xy - 3y2 = 2x2 + xy - 6xy - 3y2 = x( 2x + y ) - 3y( 2x + y ) = ( 2x + y )( x - 3y )
2) 7x2 + 3xy - 10y2 = 7x2 - 7xy + 10xy - 10y2 = 7x( x - y ) + 10y( x - y ) = ( x - y )( 7x + 10y )
3) x2 + 5x - 2 = ( x2 + 5x + 25/4 ) - 33/4 = ( x + 5/2 )2 - \(\left(\frac{\sqrt{33}}{2}\right)^2\)= \(\left(x+\frac{5}{2}-\frac{\sqrt{33}}{2}\right)\left(x+\frac{5}{2}+\frac{\sqrt{33}}{2}\right)\)
6) x4 + 324 = ( x4 + 36x2 + 324 ) - 36x2 = ( x2 + 18 )2 - ( 6x )2 = ( x2 - 6x + 18 )( x2 + 6x + 18 )
4) x8 + x7 + 1
= x8 + x7 + x6 - x6 + 1
= x6( x2 + x + 1 ) - ( x6 - 1 )
= x6( x2 + x + 1 ) - ( x3 - 1 )( x3 + 1 )
= x6( x2 + x + 1 ) - ( x - 1 )( x2 + x + 1 )( x3 + 1 )
= ( x2 + x + 1 )( x6 - ( x - 1 )( x3 + 1 ) ]
= ( x2 + x + 1 )( x6 - x4 + x3 - x + 1 )
5) x7 + x5 + 1
= x7 + x6 - x6 + x5 + 1
= x5( x2 + x + 1 ) - ( x6 - 1 )
= x5( x2 + x + 1 ) - ( x3 - 1 )( x3 + 1 )
= x5( x2 + x + 1 ) - ( x - 1 )( x2 + x + 1 )( x3 + 1 )
= ( x2 + x + 1 )[ x5 - ( x - 1 )( x3 + 1 ) ]
= ( x2 + x + 1 )( x5 - x4 + x3 - x + 1 )
7) x5 - 5x3 + 4x
= x5 - x3 - 4x3 + 4x
= x3( x2 - 1 ) - 4x( x2 - 1 )
= ( x2 - 1 )( x3 - 4x )
= ( x - 1 )( x + 1 )x( x2 - 4 )
= x( x - 1 )( x + 1 )( x - 2 )( x + 2 )
8) Xin hàng :)
a)\(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2\left(7x-4+y\right)\)
b)\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4x-8\right)\)
\(=\left(4x-8\right)\left(x^2-x-10\right)=4\left(x-2\right)\left(x^2-x-10\right)\)
a.\(7x.\left(y-4\right)^2-\left(4-y\right)^3\)=\(7x.\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2.\left(7x+y-4\right)\)
b.\(\left(4x-8\right).\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9.\left(8-4x\right)\)
=\(\left(4x-8\right)\left(x^2+6-x-7-9\right)=\left(4x-8\right)\left(x^2-x-10\right)\)
a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)
\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)
\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)
\(=\left(a+7b\right)\left(5a-b\right)\)
b) \(9x^6-12x^7+4x^8\)
\(=x^6\left(9-12x+4x^2\right)\)
\(=x^6\left(2x-3\right)^2\)
c) \(8x^6-27y^3\)
\(=\left(2x^2\right)^3-\left(3y\right)^3\)
\(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
d) \(\frac{1}{64}x^6-125y^3\)
\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)
\(=\left(\frac{1}{4}x^2-5y\right)\left(\frac{1}{16}x^4+\frac{5}{6}xy+25y^2\right)\)
a/ \(\left(a^2-b^2+1\right)\left(a^2-ab+b^2\right)\left(a^2+ab+b^2\right)\)
b/ \(\left(x+y-1\right)\left(y^2-xy+y+x^2+x+1\right)\)