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a) (x + 2)(x + 4). b) 2(x + 6)(x + l).
c) 3(3x + 5)(x + l). d) (6x -7y)(x + y).
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Bài 4:
\(x^3-2x^2+x=x\left(x-1\right)^2\)
\(5\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(5-y\right)\)
\(x^2-12x+36=\left(x-6\right)^2\)
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\(9x^2-24x+15=\left(3x\right)^2-2.3.4x+4^2-1\)
\(=\left(3x-4\right)^2-1=\left(3x-4+1\right)\left(3x-4-1\right)=\left(3x-3\right)\left(3x-5\right)\)
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a: \(x^2-6x+5=\left(x-5\right)\left(x-1\right)\)
b: \(x^2-x-12=\left(x-4\right)\left(x+3\right)\)
c: \(x^2+8x+15=\left(x+5\right)\left(x+3\right)\)
d: \(2x^2-5x-12=\left(x-4\right)\left(2x+3\right)\)
e: \(x^2-13x+36=\left(x-9\right)\left(x-4\right)\)
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\(a,=3\left(x^2-8x+16\right)=3\left(x-4\right)^2\\ b,=5\left(x^2-1\right)=5\left(x-1\right)\left(x+1\right)\\ c,=\left(x+y\right)^2-9=\left(x+y+3\right)\left(x+y-3\right)\)
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\(a,=\left(2a-1\right)\left(2a+1\right)\\ b,=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\\ c,=\left(16-3x\right)\left(16+3x\right)\\ d,Sửa:-36x^2+24x-4=-4\left(9x^2-6x+1\right)=-4\left(3x-1\right)^2\)
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a: \(=5x\left(xy^2+3x+6y^2\right)\)
b: \(=\left(x-2\right)\left(x+3\right)-\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(x+3-x-2\right)=\left(x-2\right)\)
c: \(=\left(x-3\right)\left(x-4\right)\)
d: \(=x\left(x^2-2xy+y^2-9\right)\)
=x(x-y-3)(x-y+3)
e: \(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)
f: \(=\left(x-4\right)\left(x+3\right)\)
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a: \(=4xy\left(1-5x^2y\right)\)
b: \(=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\)
c: \(=x\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(x+y\right)\)
d: \(=\left(x+2y\right)^2-36=\left(x+2y+6\right)\left(x+2y-6\right)\)
\(-36+24x-x^2\)
\(=-x^2+24x-36\)
\(=-x^2+24x-144+108\)
\(=-\left(x^2-24x+144\right)+108\)
\(=-\left(x-12\right)^2+108\le108\)
Đẳng thức xảy ra khi \(x=12\)