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a) \(81-\left(3x+2\right)^2=9^2-\left(3x+2\right)^2=\left(9-3x-2\right)\left(9+3x+2\right)=\left(7-3x\right)\left(11+3x\right)\)
b) \(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)=15\left(x-1\right)\left(3x-1\right)\)
c) \(9\left(x-5y\right)^2-16\left(x+y\right)^2=\left[3\left(x-5y\right)-4\left(x+y\right)\right]\left[3\left(x-5y\right)+4\left(x+y\right)\right]\)
\(=\left(-x-19y\right)\left(7x-11y\right)\)
Ta có:
a) 5x - 20y = 5(x - 4y)
b) 5x(x - 1) - 3x(x - 1) = x(x - 1)2
c) x(x + y) - 5x - 5y = x(x + y) - (5x + 5y) = x(x + y) - 5(x + y) = (x - 5)(x + y)
d) x2 - 9 = (x - 3)(x + 3)
e) 42 - 25 = (4 - 5)(4 + 5) f) x6 - y6 = (x4)2 - (y4)2 = (x4 - y4)(x4 + y4)
a) 5x - 20y = 5( x - 4y)
b) 5x(x-1) - 3x(x-1) =2x (x-1)
c) x2 - 9 = x2 - 32 = ( x-3)(x+3)
e) 42-25 = 42 - 52 = ( 4-5)(4+5)= -9
f) x6 - y6 = (x3)2 - (y3)2 = ( x3 - y3 ) ( x3 + y3)
= (x-y) ( x2 + xy + y2 ) ( x+y) ( x2 -xy +y2)
\(1,=\left(x-3\right)\left(x+3\right)\\ 2,=\left(x-y\right)\left(5+a\right)\\ 3,=\left(x+3\right)^2\\ 4,=\left(x-y\right)\left(10x+7y\right)\\ 5,=5\left(x-3y\right)\\ 6,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
Ta có:
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)
\(=\left(x^2+8x+2x+16\right)\left(x^2+6x+4x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+16+8\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+16\right)+8\left(x^2+10x+16\right)+16\)
\(=\left(x^2+10x+16\right)^2+2.\left(x^2+10x+16\right).4+4^2\)
\(=\left(x^2+10x+16+4\right)^2=\left(x^2+10+20\right)^2\)
k nha!!
\(\text{( x + 2 ) ( x + 4 ) ( x + 6 ) ( x + 8 ) + 16}\)
\(\text{Phân tích thành nhân tử :}\)
\(\left(x^2+10x+20\right)^2\)