Giúp mình bài này với ạ
Viết biểu thức sau dưới dạng tích:
a, (x+y+x)^2-(y+z)^2
b, (x+3^2)+4(x+3)+4
c, 25+10 (x+1)(x+1)^2
d, (x+2)^2+2(x+2)(x-2)+(x-2)^2
e,(x-3)^2-2(x^2-9)+(x+3)^2
K
Khách
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25 tháng 7 2023
2:
-8x^6-12x^4y-6x^2y^2-y^3
=-(8x^6+12x^4y+6x^2y^2+y^3)
=-(2x^2+y)^3
3:
=(1/3)^2-(2x-y)^2
=(1/3-2x+y)(1/3+2x-y)
31 tháng 8 2021
a: Ta có: \(\left(x^2+x-1\right)^2-\left(x^2+2x+3\right)^2\)
\(=\left(x^2+x-1-x^2-2x-3\right)\left(x^2+x-1+x^2+2x+3\right)\)
\(=\left(-x-4\right)\left(2x^2+3x+2\right)\)
b: Ta có: \(\left(x-3\right)^2-16\)
\(=\left(x-3-4\right)\left(x-3+4\right)\)
\(=\left(x+1\right)\left(x-7\right)\)
c: \(y^2+16y+64=\left(y+8\right)^2\)
20 tháng 8 2021
Bài 8:
Ta có: \(A=-x^2+2x+4\)
\(=-\left(x^2-2x-4\right)\)
\(=-\left(x^2-2x+1-5\right)\)
\(=-\left(x-1\right)^2+5\le5\forall x\)
Dấu '=' xảy ra khi x=1
10 tháng 12 2021
\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)
24 tháng 8 2021
a: Ta có: \(\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)+1\)
\(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\)
\(=\left(x^2+9x\right)^2+38\left(x^2+9x\right)+360+1\)
\(=\left(x^2+9x\right)^2+2\cdot\left(x^2+9x\right)\cdot19+19^2\)
\(=\left(x^2+9x+19\right)^2\)
NT
24 tháng 8 2021
b. \(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)
\(=\left(x^2+2x+1\right)+2\left(x+1\right)\left(y+1\right)+\left(y^2+2y+1\right)\)
\(=\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+1+y+1\right)^2=\left(x+y+2\right)^2\)
c. \(x^2-2x\left(y+2\right)+y^2+4y+4\)
\(=x^2-2x\left(y+2\right)+\left(y+2\right)^2\)
\(=\left(x-y-2\right)^2\)
d. \(x^2+2x\left(y+1\right)+y^2+2y+1\)
\(=x^2+2x\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+y+1\right)^2\)
a: \(\left(x+y+z\right)^2-\left(y+z\right)^2\)
\(=\left(x+y+z-y-z\right)\left(x+y+z+y+z\right)\)
\(=x\left(x+2y+3z\right)\)
b: \(\left(x+3\right)^2+4\left(x+3\right)+4\)
\(=\left(x+3+2\right)^2\)
\(=\left(x+5\right)\left(x+5\right)\)
c: \(25+10\left(x+1\right)+\left(x+1\right)^2\)
\(=\left(x+1+5\right)^2\)
\(=\left(x+6\right)\left(x+6\right)\)