Thực hiện phép tính
a) 68^2 + 64.68 + 32^2
b) ( x^3 - 6x^2 - 9x + 14 ) : ( x - 7 )
Phân tích đa thức thành nhân tử
a) 3ax - 6x - 2a^2 + 4a
b) x^3 + x^2y + 5x + 5y
c) 36a^2 - c^2 - 9b^2 - 6bc
d) x^2 - 8xy + 15y^2
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\(Bài1:\\ a,\left(4x-1\right)\left(2x^2-x-1\right)=4x\left(2x^2-x-1\right)-\left(2x^2-x-1\right)=8x^3-4x^2-4x-2x^2+x+1=8x^3-6x^2-3x+1\\ b,\left(4x^3+8x^2-2x\right):2x\\ =2x\left(2x^2+4x-1\right):2x\\ =2x^2+4x-1\)
\(Bài2:\\ a,2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\\ b,2xy+2x+yz+z=2x\left(y+1\right)+z\left(y+1\right)=\left(y+1\right)\left(2x+z\right)\\ c,x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\)
a) \(3xy\left(x-2y\right)-2x\left(x-xy\right)^2\)
\(=3x^2y-6xy^2-2x\left(x^2-2x^2y+\left(xy\right)^2\right)\)
\(=3x^2y-6xy^2-2x^3+2x^3y-2x^3y^2\)
b) \(68^2+64.68+32^2=\left(68+32\right)^2=100^2=10000\)
c) \(\left(x^3-6x^2+9x+14\right):\left(x-7\right)\)
\(=\left(x^2\left(x-7\right)-x\left(x-7\right)+2\left(x+7\right)\right):\left(x-7\right)\)
=?
a: \(=3x^2y-6xy^2-2x\left(x^2y^2-2x^2y+x^2\right)\)
\(=3x^2y-6xy^2-2x^3y^2+4x^3y-2x^3\)
b: \(=\left(68+32\right)^2=100^2=10000\)
c: \(=\dfrac{x^3-7x^2+x^2-7x+16x-112+126}{x-7}\)
\(=x^2+x+16+\dfrac{126}{x-7}\)
d: \(=15x^5-12x^4+18x^2-\dfrac{5}{4}x^4+x^3-1.5x\)
\(=15x^5-\dfrac{53}{4}x^4+x^3+18x^2-1.5x\)
e: \(=2a^2b^2+2a^2by+4axb^2+4ab^2y\)
Bài 3:
a: \(x^2-16=\left(x-4\right)\cdot\left(x+4\right)\)
b: \(x^2+2x+1-y^2=\left(x+1+y\right)\left(x+1-y\right)\)
c: \(=\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)
a) \(36a^4-y^2=\left(6a^2-y\right)\left(6a^2+y\right)\)
b) \(6x^2+x-2=2x\left(3x+2\right)-1\left(3x+2\right)=\left(3x+2\right)\left(2x-1\right)\)
Bài 2:
a: =x(x^2-25)
=x(x-5)(x+5)
b: =x(x-2y)+3(x-2y)
=(x-2y)(x+3)
c: =(2x-3)(4x^2+6x+9)+2x(2x-3)
=(2x-3)(4x^2+8x+9)
Bài 1: Thực hiện phép tính.
a) \(\left(x+2y\right)\left(x-2y\right)-5-x^2=x^2-4y^2-5-x^2=-4y^2-5\)
Bài 2: Phân tích đa thức thành nhân tử.
a) \(14x^3y^3-7x^2y+21x^2y^5=7x^2y\left(2xy^2-1+3y^4\right)\)
b) \(18x\left(1-x\right)-12y+12xy=18x\left(1-x\right)-12y\left(1-x\right)=6\left(1-x\right)\left(3x-2y\right)\)
c) \(9x^2-y^2+1-6x=\left(9x^2-6x+1\right)-y^2=\left(3x-1\right)^2-y^2=\left(3x-1-y\right)\left(3x-1+y\right)\)
Bài 1:
a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(8-2x\right)\)
\(=2\left(4-x\right)\left(2x+1\right)\)
b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
Bài 2:
a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2\left(a-b\right)\left(a-2b\right)\)
f: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
a.
\(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b.
\(x^3-9x^2+6x+16=\left(x^3-7x^2-8x\right)-\left(2x^2-14x-16\right)\)
\(=x\left(x^2-7x-8\right)-2\left(x^2-7x-8\right)\)
\(=\left(x-2\right)\left(x^2-7x-8\right)=\left(x-2\right)\left(x^2+x-8x-8\right)\)
\(=\left(x-2\right)\left[x\left(x+1\right)-8\left(x+1\right)\right]=\left(x-2\right)\left(x+1\right)\left(x-8\right)\)
c.
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10+2\right)-24\)
\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)^2-4\left(x^2+7x+10\right)+6\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10-4\right)+6\left(x^2+7x+10-4\right)\)
\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
\(68^2+64.68+32^2\)
\(=68^2+2.32.68+32^2\)
\(=\left(68+32\right)^2\)
\(=100^2\)
\(=10000\)
Mấy câu sau ai giải hộ tớ với.