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c, \(2x^2+x-3=x\left(2x-3\right)\)
d, \(6x^2-x-15=x\left(6x-15\right)\)
TK MIK NHA
\(2x^2+x-3=2x^2-2x+3x-3=2x\left(x-1\right)+3\left(x-1\right)=\left(x-1\right)\left(2x+3\right) \)
Bài làm:
1) Ta có: \(2x^2+5xy+2y^2\)
\(=\left(2x^2+4xy\right)+\left(xy+2y^2\right)\)
\(=2x\left(x+2y\right)+y\left(x+2y\right)\)
\(=\left(2x+y\right)\left(x+2y\right)\)
2) Ta có: \(2x^2+2xy-4y^2\)
\(=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)\)
\(=2x\left(x-y\right)+4y\left(x-y\right)\)
\(=2\left(x+2y\right)\left(x-y\right)\)
\(1)2x^2+5xy+2y^2=2x^2+4xy+xy+2y^2=\left(2x^2+4xy\right)+\left(xy+2y^2\right)=2x\left(x+2y\right)+y\left(x+2y\right)=\left(2x+y\right)\left(x+2y\right)\)\(2)2x^2+2xy-4y^2=2x^2+4xy-2xy-4y^2=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)=2x\left(x-y\right)+4y\left(x-y\right)=\left(2x+4y\right)\left(x-y\right)\)
\(e,x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
\(f,x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+2x\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
\(x^2-y^2+2x+1\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x+y+1\right)\)
hk tốt
^^
Phân tích đa thức thành nhân tử:
\(36-12x+x^2\)
\(=36-6x-6x+x^2\)
\(=\left(36-6x\right)-\left(6x-x^2\right)\)
\(=6\left(6-x\right)-x\left(6-x\right)\)
\(=\left(6-x\right)\left(6-x\right)=\left(6-x\right)^2\)
\(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)^2-5\left(x^2+x\right)+3\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)\left(x^2+x-5\right)+3\left(x^2+x-5\right)\)
\(=\left(x^2+x-5\right)\left(x^2+x+3\right)\)
\(\left(x^2+2x\right)^2+9x^2+18x+20\)
\(=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\)
\(=\left(x^2+2x\right)^2+5\left(x^2+2x\right)+4\left(x^2+2x\right)+20\)
\(=\left(x^2+2x\right)\left(x^2+2x+5\right)+4\left(x^2+2x+5\right)\)
\(=\left(x^2+2x+5\right)\left(x^2+2x+4\right)\)
\(2x^2-x-15\)
\(=2x\left(x-3\right)+5\left(x-3\right)\)
\(=\left(2x+5\right)\left(x-3\right)\)
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