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Bài 4 :
\(B=\left(9+1\right)\left(9^2+1\right)...\left(9^{32}+1\right)\)
\(8B=\left(9^2-1\right)\left(9^2+1\right)...\left(9^{32}+1\right)=9^{64}-1\)
\(\Rightarrow B=\frac{9^{64}-1}{8}< 9^{64}-1\Rightarrow B< C\)
a, \(A=x\left(3x+1\right)+3x+1=\left(x+1\right)\left(3x+1\right)\)
Thay x = 33 ta được : \(32.100=3200\)
b, \(B=xy+2x+2y+4=x\left(y+2\right)+2\left(y+2\right)=\left(x+2\right)\left(y+2\right)\)
Thay x = 98 ; y = 98 ta được : \(100.100=10000\)
5x2 - x3 - 12x
= x ( 5x - x2 - 12 )
= -x ( x2 - 5x + 12 )
= -x [ ( x - 5/2 )2 + 23/4 ]
d, D = 402 - 282 + 322 +80.32
D = (402 + 2.40.32 + 322) - 282
D = (40 + 32)2 - 282
D = (40 + 32 - 28)(40 + 32 + 28)
D = 44.100
D = 4400
e, E = 10.80,5 + 10.19,5 - 8.20,5 - 8. 79,5
E = 10.(80,5 + 19,5) - 8.( 20,5 + 79,5)
E = 10.100 - 8.100
E = 100.(10-8)
E = 200
F = 502 - 182 + 322 + 100.32
F = (502 - 182) + 32.( 32 + 100)
F = (50 -18)(50+18) + 32. 132
F = 32.68 + 32.132
F = 32.( 68 + 132)
F = 32. 200
F = 6400
g, sửa đề
\(5x^2-5xy+7y-7x=5x\left(x-y\right)+7\left(y-x\right)=\left(5x-7\right)\left(x-y\right)\)
h, sửa đề
\(xy-xz+z-y=x\left(y-z\right)-\left(y-z\right)=\left(x-1\right)\left(y-z\right)\)
i, \(x^3+2x^2-3x-6=x^2\left(x+2\right)-3\left(x+2\right)=\left(x^2-3\right)\left(x+2\right)\)
\(a,x^2+7x+7y-y^2\)
\(=x^2-y^2+7\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(b,x^2-2x-9y^2+6y\)
\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)
