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\(x^2-3\)
\(=x^2-\left(\sqrt{3}\right)^2\)
\(=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
\(64x^4+y^4\)
\(=\left(64x^4+16x^2y^2+y^4\right)-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
\(x^5+x-1\)
\(=x^5+x^2-\left(x^2-x+1\right)\)
\(=x^2\left(x^3+1\right)-\left(x^2-x+1\right)\)
\(=x^2\left(x+1\right)\left(x^2-x+1\right)-\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^3+x^2-1\right)\)
\(x^3\left(x^2-7\right)^2-36x\)
\(=x.\left[x^2.\left(x^2-7\right)^2-36\right]\)
\(=x.\left[\left(x^3-7x\right)^2-6^2\right]\)
\(=x.\left(x^3-7x-6\right).\left(x^3-7x+6\right)\)
\(=x.\left(x+1\right)\left(x^2-x-6\right).\left(x-1\right).\left(x^2+x-6\right)\)
\(=x.\left(x+1\right).\left(x+2\right).\left(x+3\right).\left(x-1\right).\left(x-2\right).\left(x-3\right)\)
Ta có : \(x^3\left(x^2-7\right)^2-36x\)
= \(x^3\left(x^4-14x^2+49\right)-36x\)
= \(x\left(x^6-14x^4+49x^2-36\right)\)
= \(x\left(x^2-1\right)\left(x^2-4\right)\left(x^2-9\right)\)---- chỗ này tắt
= (x-3)(x-2)(x-1)x(x+1)(x+2)(x+3)
a)A=(x2+2x)+9x2+18x+20
=(x2+2x)+9(x2+2x)+20
Đặt t=x2+2x đc:
t+9t+20=10t+20=10(t+2)
Thay t=x2+2x vào đc:
10(x2+2x+2)
\(x^5+y^5-\left(x+y\right)^5\)
\(=x^5+y^5-\left(x^5+5x^4y+10x^3y^2+10x^2y^3+8xy^4+y^5\right)\)
\(=-5xy\left(x^3+2x^2y+2xy^2+y^3\right)\)
\(=-5xy\left[\left(x+y\right)\left(x^2-xy+y^2\right)+2xy\left(x+y\right)\right]\)
\(=-5xy\left(x+y\right)\left(x^2+xy+y^2\right)\)