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f: B-A=21/4xy^3-7/6x^3y-5xy^3+5/8x^3y=1/4xy^3-13/24x^3y
=>A-B=13/24x^3y-1/4xy^3
f: B-A=21/4xy^3-7/6x^3y-5xy^3+5/8x^3y=1/4xy^3-13/24x^3y
=>A-B=13/24x^3y-1/4xy^3
a: A+2xy^2-x^2y-B=3x^2y-4xy^2
=>A-B=3x^2y-4xy^2-2xy^2+x^2y=4x^2y-6xy^2
=>A=4x^2y; B=6xy^2
b: 5xy^2-A-6x^2y+B=-7xy^2+8x^2y
=>-A+B=-7xy^2+8x^2y-5xy^2+6x^2y=14x^2y-12xy^2
=>A=12xy^2; B=14x^2y
c: 5xy^3-A-5/8x^3y+B=2+1/4xy^3-7/6x^3y
=>-A+B=2+1/4xy^3-7/6x^3y-5xy^3+5/8x^3y
=>B-A=-19/4xy^3-13/24x^3y+2
=>B=-19/4xy^3; A=13/24x^3y-2
\(3x^2\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\left(3x^2+2y^2\right)\)
\(=9x^4-6x^2y^2-9x^4+4y^4\)
\(=-6x^2y^2+4y^4\)
Bài 1:
a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(8-2x\right)\)
\(=2\left(4-x\right)\left(2x+1\right)\)
b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
Bài 2:
a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2\left(a-b\right)\left(a-2b\right)\)
f: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
\(3x^2\cdot\left(3x^2-2y^2\right)-\left(3x^2-2y^2\right)\cdot\left(3x^2+2y^2\right)\)
\(\Leftrightarrow\left(3x^2-2y^2\right)\cdot\left(3x^2-3x^2+2y^2\right)\)
\(\Leftrightarrow2y^2\cdot\left(3x^2-2y^2\right)\)
\(\Leftrightarrow6x^2y^2-4y^4\)
\(\left(3x^2-5xy^3\right)\left(3x^2+5xy^3\right)\)
\(=\left(3x^2\right)^2-\left(5xy^3\right)^2\)
\(=9x^4-25x^2y^6\)
\(\left(3x^2-5xy^3\right)\left(3x^2+5xy^3\right)\\ =9x^4-25x^2y^6\)