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(x2-8)2+36=x4-16x2+100=x4+20x2+100-36x2=(x2+10)2-36x2=(x2+10-6x)(x2+10+6x)
x^2 - y^2 + 12y - 36
= x^2 - (y^2 - 12y +36)
=x^2 - (y-6)^2
= (x-y+6) ( x+y-6)
A= \(x.\left\{\left[x.\left(x^2-7\right)\right]^2-6^2\right\}=x.\left[x.\left(x^2-7\right)-6\right].\left[x.\left(x^2-7\right)+6\right]\)
A=\(x.\left[x^3-7x-6\right].\left[x^3-7x+6\right]\)
A= \(x.\left(x-3\right).\left(x+1\right).\left(x+2\right).\left(x+3\right).\left(x-1\right).\left(x-2\right)\)
\(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+64+36\)
\(=x^4-16x^2+100\)
\(=x^4+20x^2+100-36x^2\)
\(=\left(x^2+10\right)^2-36x^2\)
\(=\left(x^2+10-6x\right)\left(x^2+10+6x\right)\)
( x2 - 8)2 + 36 = x4 -16x2 +64 + 36
= (x4 +20x2 +100) -36x2
=( x2+10)2 -(6x)2
=(x2 + 10 -6x)(x2 +10 +6x)
\(36\left(a-b\right)^2-25\left(2a-1\right)^2=\left[6\left(a-b\right)\right]^2-\left[5\left(2a-1\right)\right]^2\)
\(=\left(6a-6b\right)^2-\left(10a-5\right)^2=\left(6a-6b-10a+5\right)\left(6a-6b+10a-5\right)\)
\(=\left(-4a-6b+5\right)\left(16a-6b-5\right)\)
Ta có :
\(36\left(a-b\right)^2-25\left(2a-1\right)^2\)
\(=\left[6\left(a-b\right)\right]^2-\left[5\left(2a-1\right)\right]^2\)
\(=\left[6\left(a-b\right)+5\left(2a-1\right)\right]\left[6\left(a-b\right)-5\left(2a-1\right)\right]\)
\(=\left(6a+6b+10a-5\right)\left(6a+6b-10a+5\right)\)
\(=\left(16a+6b-5\right)\left(6b-4a+5\right)\)
\(36^2+26^2-52\cdot36\)
= \(36^2-2\cdot36\cdot26+26^2\)
= \(\left(36-26\right)^2\)
= \(10^2\)=\(100\)