Question

cần gấp ạ

Answer 1

1.

a. 3xy+6xz=3x(y+2z)

b. \(18x^2y-12x^3=6x^2\left(3y-2x\right)\)

\(8xy^2-2x^2y=2xy\left(4y-x\right)\)

\(3xy^2+6xy=3xy\left(y+2\right)\)

2.

a. \(x\left(x+y\right)-7x-7y=x\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(x-7\right)\)

b. \(x^2\left(x-y\right)+2x-2y=x^2\left(x-y\right)+2\left(x-y\right)=\left(x-y\right)\left(x^2+2\right)\)

c. \(x\left(x+3y\right)-5x-15y=x\left(x+3y\right)-5\left(x+3y\right)=\left(x+3y\right)\left(x-5\right)\)

d. \(2x\left(x-5\right)+3x-15=2x\left(x-5\right)+3\left(x-5\right)=\left(x-5\right)\left(2x+3\right)\)

e. \(x\left(x+y\right)+ax+ay=x\left(x+y\right)+a\left(x+y\right)=\left(x+y\right)\left(x+a\right)\)

f. \(a\left(x+y\right)-4x-4y=a\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(a-4\right)\)

3.

a.

\(\left(3x+1\right)^2-\left(x+1\right)^2=\left\lbrack\left(3x+1\right)-\left(x+1\right)\right\rbrack\left\lbrack\left(3x+1\right)+\left(x+1\right)\right\rbrack=2x\left(4x+2\right)\)

b.

\(\left(x+y\right)^2-\left(x-y\right)^2=\left\lbrack\left(x+y\right)-\left(x-y\right)\right\rbrack\left\lbrack\left(x+y\right)+\left(x-y\right)\right\rbrack=2y.2x=4xy\)

c.

\(9\left(x-y\right)^2-4\left(x+y\right)^2=\left(3x-3y\right)^2-\left(2x+2y\right)^2\)

\(=\left\lbrack\left(3x-3y\right)-\left(2x+2y\right)\right\rbrack\left\lbrack\left(3x-3y\right)+\left(2x+2y\right)\right\rbrack=\left(x-5y\right)\left(5x-y\right)\)

d.

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

\(=\left(x+y\right)\left(5x-5y\right)=5\left(x-y\right)\left(x+y\right)\)