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\(2a^2+8b^2-8ab\)
\(=2\left(a^2-4ab+4b^2\right)\)
\(=2\left(a-2b\right)^2\)
\(=4\left[a^2-\left(b^2-4bc+4c^2\right)\right]\)
\(=4\left[a^2-\left(b-2c\right)^2\right]\)
\(=4\left(a-b+2c\right)\left(a+b-2c\right)\)
\(4a^2-4b^2+16bc-16c^2\)
\(=4a^2-\left(4b^2-16bc+16c^2\right)\)
\(=\left(2a\right)^2-\left[\left(2b\right)^2-2.2b.4c+\left(4c\right)^2\right]\)
\(=\left(2a\right)^2-\left(2b-4c\right)^2\)
\(=\left(2a+2b-4c\right)\left(2a-2b+4c\right)\)
\(=4\left(a+b-c\right)\left(a-b+c\right)\)
d) (8a3 – 27b3) – 2a(4a2 – 9b2)
= (2a – 3b)(4a2 + 6ab + 9b2) – 2a(2a – 3b)(2a + 3b)
= (2a – 3b)(4a2 + 6ab + 9b2 – 4a2 – 6ab) = 9b2(2a – 3b)
\(a^2-2.a.2b+4b^2-5b^2=\left(a-2b\right)^2-5b^2..\)
\(=\left(a-2b-b\sqrt{5}\right)\left(a-2b+b\sqrt{5}\right)\)
\(a,x^2-4xa+4a^2-81y^2=\left(x-2a\right)^2-\left(9y\right)^2=\left(x-2a-9y\right)\left(x-2a+9y\right)\\ b,3x^2-8x+4=\left(3x^2-6x\right)-\left(2x-4\right)=3x\left(x-2\right)-2\left(x-2\right)=\left(x-2\right)\left(3x-2\right)\)
\(a,=\left(2a-1\right)\left(2a+1\right)\\ b,=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\\ c,=\left(16-3x\right)\left(16+3x\right)\\ d,Sửa:-36x^2+24x-4=-4\left(9x^2-6x+1\right)=-4\left(3x-1\right)^2\)
a: \(x^2-y^2+10yz-25z^2\)
\(=x^2-\left(y^2-10yz+25z^2\right)\)
\(=x^2-\left(y-5z\right)^2\)
\(=\left(x-y+5z\right)\left(x+y-5z\right)\)
4.(a2-ab-b2)
\(4a^2-4ab-8b^2\)
\(=4\left(a^2-ab-2b^2\right)\)
\(=4\left(a^2-ab-b^2-b^2\right)\)
\(=4\left[\left(a^2-b^2\right)-\left(ab+b^2\right)\right]\)
\(=4\left[\left(a-b\right)\left(a+b\right)-b\left(a+b\right)\right]\)
\(=4\left(a+b\right)\left(a-b-b\right)\)
\(=4\left(a+b\right)\left(a-2b\right)\)