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a, \(\left(5x-4\right)\left(5x+4\right)-\left(5x-4\right)^2=\left(25x^2-16\right)-\left(25x^2-40x+16\right)=40x-32\)
b,\(\left(5x+3\right)^2-\left(4x-1\right)^2-\left(9x^2+8\right)=\left(x+4\right)\left(9x-2\right)-\left(9x^2+8\right)\)
\(=9x^2+34x-8-\left(9x^2+8\right)=34x\)
c,\(2\left(x-5y\right)\left(x+5y\right)+\left(x+5y\right)^2+\left(x-5y\right)^2=\left(2x\right)^2=4x^2\)
Bài 1
\(x^3-4x^2+8x-8=\left(x^3-8\right)-4x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4-4x\right)=\left(x-2\right)\left(x^2-2x+4\right)\)
Bài 2
\(a^2+b^2-a^2b^2+ab-a-b\)
\(=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)\)
\(=a^2\left(1-b\right)\left(1+b\right)+\left(a+b\right)\left(b-1\right)\)
\(=-a^2\left(b-1\right)\left(b+1\right)+\left(a+b\right)\left(b-1\right)\)
\(=\left(b-1\right)\left[a+b-a^2\left(b+1\right)\right]\)
\(=\left(b-1\right)\left(a+b-a^2b-a^2\right)\)
\(=\left(b-1\right)\left[\left(a-a^2\right)+b\left(1-a^2\right)\right]\)
\(=\left(b-1\right)\left[a\left(1-a\right)+b\left(1-a\right)\left(1+a\right)\right]\)
\(=\left(b-1\right)\left(1-a\right)\left[a+b\left(1+a\right)\right]\)
\(=\left(b-1\right)\left(1-a\right)\left(a+b+ab\right)\)
Bài 3
\(3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-z\right)\left(x+y+z\right)\)
Bài 4
\(5x\left(x-2\right)-3x^2\left(x-2\right)=x\left(x-2\right)\left(5-3x\right)\)
\(3x\left(x-5y\right)-2y\left(5y-x\right)=3x\left(x-5y\right)+2y\left(x-5y\right)=\left(3x+2y\right)\left(x-5y\right)\)
`@` `\text {Ans}`
`\downarrow`
`A - B`
`= (x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2) - (x^2y^4 + 5xy^3 + x^5y^2)`
`= x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2 - x^2y^4 - 5xy^3 - x^5y^2`
`= (x^5y^2 - x^5y^2) + (7x^2y^4 - x^2y^4) + (5xy^3 - 5xy^3) + xy + 2`
`= 6x^2y^4 + xy + 2`
a) 2x-5y+4y+2x
=4x+y
Tai x=3 y=-12 thi
4x3+(-12)=12-12=0
b)3x+4y-2x-3y