Question

phân tích đa thức thành nhân tử

a)(2a+3)*x-(2a+3)*y+(2a+3)

b)(4x-y)*(a-1)-(y-4x)*(b-1)+(4x-y)*(1-c)

c)x^k+1-x^k-1(k thuộc N,k>1)

d)x^m+3-x^m+1(m thuộc N)

e)3*(x-y)^3-2*(x-y)^2

f)81a^2+18a+1

g)25a^2*b^2-16c^2

h)(a-b)^2-2*(a-b)*c+c^2

i)(ax+by)^2-(ax-by)^2

Answer 1

\(a,\left(2a+3\right)x-\left(2a+3\right)y+\left(2a+3\right)\)

\(=\left(2a+3\right)\left(x-y+1\right)\)

\(b,\left(4x-y\right)\left(a-1\right)-\left(y-4x\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

​\(=\left(4x-y\right)\left(a-1\right)+\left(4x-y\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)​

\(=\left(4x-y\right)\left(a-1+b-1+1-c\right)\)

\(=\left(4x-y\right)\left(a+b-c-1\right)\)

\(c,x^k+1-x^k-1\)

\(=0?!?!\)

\(d,x^m+3-x^m+1\)

\(=4\)

\(e,3\left(x-y\right)^3-2\left(x-y\right)^2\)

\(=\left(x-y\right)^2\left(3\left(x-y\right)-2\right)\)

\(=\left(x-y\right)^2\left(3x-3y-2\right)\)

Answer 2

\(f,81a^2+18a+1\)

\(=\left(9a\right)^2+2.9a+1\)

\(=\left(9a+1\right)^2\)

\(g,25a^2.b^2-16c^2\)

\(=\left(5ab\right)^2-\left(4c\right)^2\)

\(=\left(5ab+4c\right)\left(5ab-4c\right)\)

\(h,\left(a-b\right)^2-2\left(a-b\right)c+c^2\)

\(=\left(a-b-c\right)^2\)

\(i,\left(ax+by\right)^2-\left(ax-by\right)^2\)

\(=\left(ax+by-ax+by\right)\left(ax+by+ax-by\right)\)

\(=2by.2ax\)

\(=4axby\)

Answer 3

\(\text{a) }\left(2a+3\right)x-\left(2a+3\right)y+\left(2a+3\right)\)

\(=\left(2a+3\right)\left(x-y+1\right)\)

\(\text{b) }\left(4x-y\right)\left(a-1\right)-\left(y-4x\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

\(=\left(4x-y\right)\left(a-1\right)+\left(4x-y\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

\(=\left(4x-y\right)\left(a-1+b-1+1-c\right)\)

\(=\left(4x-y\right)\left(a+b-c-1\right)\)

\(\text{c) }x^k+1-x^k-1\)

\(=\left(x^k-x^k\right)+\left(1-1\right)\)

\(=0\)

\(\text{d) }x^m+3-x^m+1\)

\(=\left(x^m-x^m\right)+\left(3+1\right)\)

\(=4\)

\(\text{e) }3\left(x-y\right)^3-2\left(x-y\right)^2\)

\(=\left(x-y\right)^2\left[3\left(x-y\right)-2\right]\)

\(=\left(x-y\right)^2\left(3x-3y-2\right)\)

\(\text{f) }81a^2+18a+1\)

\(=\left(9a\right)^2+2.9a.1+1^2\)

\(=\left(9a+1\right)^2\)

\(\text{g) }25a^2b^2-16c^2\)

\(=\left(5ab\right)^2-\left(4c\right)^2\)

\(=\left(5ab+4c\right)\left(5ab-4c\right)\)

\(\text{h) }\left(a-b\right)^2-2.\left(a-b\right).c+c^2\)

\(=\left(a-b-c\right)^2\)

\(\text{i) }\left(ax+by\right)^2-\left(ax-by\right)^2\)

\(=\left(ax+by+ax-by\right)\left(ax+by-ax+by\right)\)

\(=2by.2ax\)

\(=4byax\)