\(8x^3+60x^2y+150xy^2+125y^3=\left(2x\right)^3+3.\left(2x\right)^2.5y+3.2x.\left(5y\right)^2+\left(5y\right)^3\)

\(=\left(2x+5y\right)^3\)

a: \(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

c: \(x^3-125=\left(x-5\right)\left(x^2+5x+25\right)\)

\(\dfrac{1}{8}x^3-64=\left(\dfrac{1}{2}x-4\right)\left(\dfrac{1}{4}x^2+2x+16\right)\)

d: \(=\left(2x+5y\right)^3\)

\(8x^3+60x^2y+150xy^2+125y^3\)

\(=\left(8x^3+125y^3\right)+\left(60x^2y+150xy^2\right)\)

\(=\left(2x+5y\right)\left(4x^2-10xy+25y^2\right)+30xy\left(2x+5y\right)\)

\(=\left(2x+5y\right)\left(4x^2-10xy+25y^2+30xy\right)\)

\(=\left(2x+5y\right)\left(4x^2+20xy+25y^2\right)\)

\(=\left(2x+5y\right)\left(2x+5y\right)^2=\left(2x+5y\right)^3\)

C2 : Áp dụng luôn HĐT ( x + y ) ³

\(8x^3+60x^2y+150xy^2+125y^3\)

\(=\left(2x\right)^3+3.\left(2x\right)^2.5y+3.2x.\left(5y\right)^2+\left(5y\right)^3\)

\(=\left(2x+5y\right)^2\)

=.= hok tốt!!

1.\(x^{16}-y^{16}=\left(x^8-y^8\right)\left(x^8+y^8\right)\)

2.\(x^3-125=x^3-5^3=\left(x-5\right)\left(x^2+5x+25\right)\)

\(-64+\frac{1}{8}x^3=\left(\frac{x}{2}\right)^3-4^3=\left(\frac{x}{2}-4\right)\left(\frac{x^2}{4}+2x+16\right)\)

\(8x^3+60x^2y+150xy^2+125y^3=\left(2x\right)^3+3.\left(2x\right)^2.\left(5y\right)+3.\left(2x\right).\left(5y\right)^2+\left(5y\right)^3\)

\(=\left(2x+5y\right)^3\)

cám ơn bn Nguyễn Minh Quang nhé

!!

a) Ta có : 64x² - (8x + y)² 

= (8x)² - (8x + y)² 

= (8x - 8x - y) (8x + 8x + y)

= -y(16x + y)

Bài 1:

a)\(64x^2-(8x+y)^2=-y\left(16x+y\right)\)

b)\((x+y+15)^2-2(x+y+15)+1\)

\(=\left(x+y+14\right)^2\)

c)\(8x^3+60x^2y+150xy^2+125y^3\)

\(=\left(2x+5y\right)^3\)

d)\(x^{16}-1\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)

Bài 2:

\(\left(n+7\right)^2-\left(n-5\right)^2\)

\(=\left(n+7+n+5\right)\left(n+7-\left(n+7\right)\right)\)

\(=24\left(n+1\right)\) chia hết 24

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