Question

cần gấp ạ

Answer 1

Bài 5:

1: \(9-\left(x-y\right)^2\)

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

=(3-x+y)(3+x-y)

2: \(\left(x-y\right)^2-4\)

\(=\left(x-y\right)^2-2^2\)

=(x-y-2)(x-y+2)

3: \(\left(x+2\right)^2-y^2\)

=(x+2-y)(x+2+y)

4: \(\left(x+5\right)^2-y^2=\left(x+5+y\right)\left(x+5-y\right)\)

5: \(\left(x+y\right)^2-9x^2\)

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

=(x+y-3x)(x+y+3x)

=(-2x+y)(4x+y)

6: \(16x^2-\left(x+1\right)^2\)

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

=(4x-x-1)(4x+x+1)

=(3x-1)(5x+1)

Bài 4:

1: \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)

2: \(x^2-16y^2=x^2-\left(4y\right)^2=\left(x-4y\right)\left(x+4y\right)\)

3: \(9x^2-1=\left(3x\right)^2-1^2=\left(3x-1\right)\left(3x+1\right)\)

4: \(x^2+6x+9=x^2+2\cdot x\cdot3+3^2=\left(x+3\right)^2\)

5: \(4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\)

6: \(10x-x^2-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)

7: \(1-8x^3=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

8: \(x^3+27=x^3+3^3=\left(x+3\right)\left(x^2-3x+9\right)\)

9: \(8x^3-y^3=\left(2x\right)^3-y^3=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

Bài 3:

1: \(ax-bx-2cx-2a+2b+4c\)

=x(a-b-2c)-2(a-b-2c)

=(a-b-2c)(x-2)

2: \(3a\cdot x^2+3b\cdot x^2+ax+bx+5a+5b\)

\(=3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\)

\(=\left(a+b\right)\cdot\left(3x^2+x+5\right)\)

3: \(ax^2-bx^2-2ax+2bx-3a+3b\)

\(=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2-2x-3\right)=\left(x-3\right)\left(x+1\right)\left(a-b\right)\)

Bài 2:

1: \(x^2+xy-xz-yz\)

=x(x+y)-z(x+y)

=(x+y)(x-z)

2: \(xy+xz+3y+3z\)

=x(y+z)+3(y+z)

=(y+z)(x+3)

3: \(x^2-3x+xy-3y\)

=x(x-3)+y(x-3)

=(x-3)(x+y)

4: \(xy-3x-y^2+3y\)

=x(y-3)-y(y-3)

=(y-3)(x-y)

5: \(x^2+2x-xy-2y\)

=x(x+2)-y(x+2)

=(x+2)(x-y)

6: \(3x^2-x-3xy+y\)

=x(3x-1)-y(3x-1)

=(3x-1)(x-y)

7: \(x^2+ab+ax+bx\)

\(=x\left(x+a\right)+b\cdot\left(x+a\right)\)

=(x+a)(x+b)

8: \(ax-bx+ab-x^2\)

\(=ax-x^2+ab-bx\)

=x(a-x)+b(a-x)

=(a-x)(x+b)

Bài 1:

1: 2x(x-5)+3x-15

=2x(x-5)+3(x-5)

=(x-5)(2x+3)

2: \(x\left(x+y\right)+ax+ay\)

=x(x+y)+a(x+y)

=(x+y)(x+a)

3: a(x+y)-4x-4y

=a(x+y)-4(x+y)

=(x+y)(a-4)

4: a(x-y)+bx-by

=a(x-y)+b(x-y)

=(x-y)(a+b)

5: xy+yz-5(x+y)

=z(x+y)-5(x+y)

=(x+y)(z-5)

6: 5(x-y)+ax-ay

=5(x-y)+a(x-y)

=(x-y)(a+5)