Question

Answer 1

1) Ta có: \(5x^2y\left(x-7\right)-5xy\left(7-x\right)\)

\(=5x^2y\left(x-7\right)+5xy\left(x-7\right)\)

\(=5xy\left(x-7\right)\left(x+1\right)\)

2) Ta có: \(3ab\left(x-y\right)+3a\left(y-x\right)\)

\(=3ab\left(x-y\right)-3a\left(x-y\right)\)

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

3) Ta có: \(4a\left(x-5\right)-2\left(5-x\right)\)

\(=4a\left(x-5\right)+2\left(x-5\right)\)

\(=2\left(x-5\right)\left(2a+1\right)\)

Answer 2

1) 5x²y(x -7) -5xy(7 -x)

<=> 5x²y(x -7) -5xy( -x +7)

<=> 5x²y(x -7) +5xy(x -7)

<=> (x -7)(5x²y -5xy) <=>5xy(x -7)(x -1)

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

<=> 3ab(x -y) +3a(-x +y)

<=> 3ab(x -y) -3a(x -y)

<=> (x -y)(3ab -3a) <=>3a(x -y)(b -1)

3) 4a(x -5) -2(5 -x)

<=> 4a(x -5) -2(-x +5)

<=> 4a(x -5) +2(x -5)

<=> (x -5)(4a +2) <=>2(x -5)(2a +1)

Answer 3

\(4,-3a\left(x-3\right)-a^2\left(3-x\right)\\ =-3a\left(x-3\right)+a^2\left(x-3\right)\\ =\left(x-3\right)\left(a^2-3a\right)\\ =a\left(x-3\right)\left(a-3\right)\\ 5,2a^2b\left(x+y\right)-4a^3b\left(-x-y\right)\\ ==2a^2b\left(x+y\right)+4a^3b\left(x+y\right)\\ =\left(x+y\right)\left(2a^2b+4a^3b\right)\\ =\left(x+y\right)2a^2b\left(1+a\right)\\ 6,7a\left(x-2y\right)-14a^2\left(2y-x\right)\\ =7a\left(x-2y\right)+14a^2\left(x-2y\right)\\ =\left(x-2y\right)\left(7a+14a^2\right)\\ =\left(x-2y\right)7a\left(1+2a\right)\)

Answer 4

4) -3a(x -3) -a²(3 -x)

<=> -3a(-3 +x) -a²(3 -x)

<=> 3a(3 -x) -a²(3 -x)

<=> (3 -x)(3a -a²) <=>a(3 -x)(3 -a)

5) 2a²b(x +y) -4a³b(-x -y)

<=> 2a²b(x +y) +4a³b(x +y)

<=> (x +y)(2a²b +4a³b)

<=> 2ab(x +y)(a +2a²)

<=> 2a²b(x +y)( 1 +2a)