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\(-3x^2+4x-2020\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{2020}{3}\right)\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{4}{9}+\frac{6056}{9}\right)\)
\(=-3\left[\left(x-\frac{2}{3}\right)^2+\frac{6056}{9}\right]\)
\(=-3\left(x-\frac{2}{3}\right)^2-\frac{6056}{3}\ge-\frac{6056}{3}\)
(Dấu "=" \(\Leftrightarrow x-\frac{2}{3}=0\Leftrightarrow x=\frac{2}{3}\))
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)
Đặt \(x^2+7x=t\)
\(\left(t+10\right)\left(t+12\right)-8=t^2+22t+120-8\)
\(=t^2+22t+112=\left(t+8\right)\left(t+14\right)\)
Theo cách đặt \(=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)
\(x^2\left(x-3\right)^2-\left(x-3\right)^2-x^2+1=\left(x-3\right)^2\left(x^2-1\right)-\left(x^2-1\right)=\left(x^2-1\right)\left(x-3\right)^2=\left(x-1\right)\left(x+1\right)\left(x-3\right)^2\)
a: =xy(x^2-4xy^2+4y^4)
=xy(x-2y^2)^2
b:=(x^3-y)^2
c: =(a^2-b^2)(a^2+b^2)
=(a^2+b^2)(a-b)(a+b)
d: 64x^6-27y^6
=(4x^2-3y^2)(16x^4+12x^2y^2+9y^4)
e: =(2x)^3+(3y)^3
=(2x+3y)(4x^2-6xy+9y^2)
a: \(=5y^2\left(5x+3\right)\)
b: \(=6x\left(x-y\right)+3y\left(x-y\right)\)
\(=3\left(x-y\right)\left(2x+y\right)\)
a) -4x2 + 8x - 4
= - (4x2 - 8x + 4)
= - (2x - 2)2
b) -x52 + 10 x - 5
= - 5(x2 - 2x + 1)
= - 5(x - 1)2
(a+b)3-(a-b)3=a3+3a2b+3ab2+b3-(a3-3a2b+3ab2-b3)
=a3+3a2b+3ab2+b3-a3+3a2b-3ab2+b3
=6a2b+2b3
Áp dụng hđt a3-b3=(a-b)(a2+ab+b2) ấy
\(\left(a+b\right)^3-\left(a-b\right)^3=\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=\left(a+b-a+b\right)\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)
\(=2b\left(3a^2+b^2\right)\)
\(a,=\left(x-3\right)\left(x+3\right)\\ b,=\left(2x-5\right)\left(2x+5\right)\\ c,=\left(x^3-y^3\right)\left(x^3+y^3\right)\\ =\left(x-y\right)\left(x+y\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\\ d,=\left(3x+y\right)^2\\ e,=-\left(x-3\right)^2\\ f,=\left(x+2y\right)^2\)
\(a.\\ x^2-9=\left(x-3\right)\left(x+3\right)\\ b.\\ 4x^2-25=\left(2x\right)^2-5^2\\ =\left(2x-5\right)\left(2x+5\right)\\ c.\\ x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3\\ =\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)\\ =\left(x-y\right)\left(x+y\right)\left(x^2+y^2+xy\right)\left(x^2+y^2-xy\right)\\ \)
\(d.\\ 9x^2+6xy+y^2=\left(3x\right)^2+2\cdot3\cdot x\cdot y+y^2\\ =\left(3x+y\right)^2\\ e.\\ 6x-9-x^2=-\left(x^2-6x+9\right)\\=-\left(x-3\right)^2\\ f.\\ x^2+4y^2+4xy=x^2+4xy+\left(2y\right)^2=\left(x+2y\right)^2\)