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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: \(=\left(2x+5y\right)^3\)
!!
\(8x^3+60x^2y+150xy^2+125y^3=\left(2x\right)^3+3.\left(2x\right)^2.5y+3.2x.\left(5y\right)^2+\left(5y\right)^3\)
\(=\left(2x+5y\right)^3\)
a) 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
1) \(\dfrac{1}{27}+a^3=\left(\dfrac{1}{3}+a\right)\left(\dfrac{1}{9}-\dfrac{a}{3}+a^2\right)\)
2) \(=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
3) \(=\left(\dfrac{1}{2}x+2y\right)\left(\dfrac{1}{4}x-xy+4y^2\right)\)
4) \(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
5) \(=\left(x^3+1\right)\left(x^6-x^3+1\right)\)
6) \(=\left(x-4\right)\left(x^2+4x+16\right)\)
7) \(=\left(x-5\right)\left(x^2+5x+25\right)\)
8) \(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
9) \(=\left(\dfrac{1}{4}x^2-5y\right)\left(\dfrac{1}{16}x^4+\dfrac{5}{4}x^2y+25y^2\right)\)
10) \(=\left(\dfrac{1}{2}x-2\right)\left(\dfrac{1}{4}x^2+x+4\right)\)
11) \(=\left(x+2\right)^3\)
12) \(=\left(x+3\right)^3\)
Làm bài 1 thôi !! Mấy bài kia tương tự . Tìm nhân tử chung ra .
a) \(m^2-n^2=\left(m-n\right)\left(m+n\right)\)
b) \(\left(x^2+x-1\right)^2-\left(x^2+2x+3\right)^2=\left(x^2+x-1+x^2+2x+3\right)\left(x^2+x-1-x^2-2x-3\right)\)
\(=\left(2x^2+3x+2\right)\left(-x-4\right)\)
c) \(-16+\left(x-3\right)^2=\left(x-3+4\right)\left(x-3-4\right)=x\left(x-7\right)\)
d) \(64+16y+y^2=\left(y+8\right)\left(y+8\right)\)
a) = (3x)^2 + 2.3x.5+ 5^2 = (3x+5)^2
b) = (2/3x)^2-(4y)^2=(2/3x-4y)(2/3x+4y)
c) = -(9x^4-12/5x^2y^2+4/25y^4) = -[(3x^2)^2 - 2.3x^2.2/5y^2 + (2/5y^2)^2]= -(3x^2-2/5y^2)^2
d) = (x-5)^2 - 4^2= (x-5+4)(x-5-4) = (x-1)(x-9)
e) = (2x)^3 + 3.(2x)^2.(5y) + 3.(2x).(5y)^2 + (5y)^3 = (2x+5y)^3
f) = (8x)^2 - (8a+b)^2 = (8x-8a-b)(8x+8a+b)
g) = (7x-4-2x-1)(7x-4+2x+1) = (5x-5)(9x-3) = 5(x-1).3(x-3)=15(x-1)(x-3)
h) = (x-y)(x+y)- 2(x+y) = (x+y)(x-y-2)
# Chúc bạn học 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