a) \(\left(2a-b\right)\left(b+4a\right)+2a\left(b-3a\right)\)

\(=2ab+8a^2-b^2-4ab+2ab-6a^2\)

\(=\left(2ab+2ab-4ab\right)+\left(8a^2-6a^2\right)-b^2\)

\(=2a^2-b^2\)

b) \(\left(3a-2b\right).\left(2a-3b\right)-6a\left(a-b\right)\)

\(=6a^2-9ab-4ab+6b^2-6a^2+6ab\)

\(=\left(6a^2-6a^2\right)-\left(9ab+4ab-6ab\right)+6b^2\)

\(=-7ab+b^2\)

c) \(5b\left(2x-b\right)-\left(8b-x\right)\left(2x-b\right)\)

\(=10bx-5b^2-\left(16bx-8b^2-2x^2+bx\right)\)

\(=10bx-5b^2-16bx+8b^2+2x^2-bx\)

\(=\left(10bx-16bx-bx\right)-\left(5b^2-8b^2\right)+2x^2\)

\(=-7bx+3b^2+2x^2\)

d) \(2x\left(a+15x\right)+\left(x-6a\right)\left(5a+2x\right)\)

\(=2ax+30x^2+5ax+2x^2-30a^2-12ax\)

\(=\left(2ax+5ax-12ax\right)+\left(30x^2+2x^2\right)-30a^2\)

\(=-5ax+32x^2-30a^2\)

a: =2ab+8a^2-b^2-4ab+2ab-6a^2

=2a^2-b^2

b: =6a^2-9ab-4ab+6b^2-6a^2+6ab

=-7ab+6b^2

c: =10bx-5b^2-16bx+8b^2+2x^2-xb

=3b^2+2x^2-7xb

d: =2xa+30x^2+5ax+2x^2-30a^2-12ax

=32x^2-30a^2-5ax

a)  (2a - b)(b + 4a) + 2a(b - 3a)
= 2a(b + 4a) - b(b + 4a) + 2ab - 6a^2
= 2ab + 8a^2 - b^2 - 4ab + 2ab - 6a^2
= (8a^2 - 6a^2) + (2ab + 2ab - 4ab) - b^2
= 2a^2 - b^2
b) .(3a - 2b)(2a - 3b) - 6a(a - b)
= 3a(2a - 3b) - 2b(2a - 3b) - (6a^2 - 6ab)
= 6a^2 - 9ab - (4ab - 6b^2) - (6a^2 - 6ab)
= 6a^2 - 9ab - 4ab + 6b^2 - 6a^2 + 6ab
= 6b^2 + (6a^2 - 6a^2) + (6ab - 4ab - 9ab)
= 6b^2 - 7ab

c. 5b(2x - b) - (8b - x)(2x - b)
= 10bx - 5b^2 - 8b(2x - b) + x(2x - b)
= 10bx - 5b^2 - 16bx + 8b^2 + 2x^2 - bx
= (10bx - 16bx - bx) + 2x^2 + (8b^2 - 5b^2)
= -7bx + 2x^2 + 3b^2
d. 2x(a + 15x) + (x - 6a)(5a + 2x)
= 2ax + 30x^2 + x(5a + 2x) - 6a(5a + 2x)
= 2ax + 30x^2 + 5ax + 2x^2 - 30a^2 - 12ax
= (30x^2 + 2x^2) + (2ax + 5ax - 12ax) - 30a^2
= 32x^2 - 5ax - 30a^2

Chúc bạn hok tốt !!!

1) (a+2b+1)2

=a2+2a(2b+1)+(2b+1)2

=a2+4ab+2a+(2b)2+2.2b.1+12

=a2+4ab+2a+4b2+4b+1

2) (2a-b+3)2

=(2a)2 -2.2a(b-3)+(b-3)2

=4a2-4a(b-3)+b2-2b.3+32

=4a2-4ab+12a+b2 -6b+9

3) (2a-3b+1)2

=(2a)2-2.2a(3b-1)+(3b-1)2

=4a2-4a(3b-1)+(3b)2-2.3b.1+12

=4a2-4ab+4a+9b2-6b+1

a/ (3x+a)(2x-5a)-6a(2x-a)

=6x\(^2\)-15ax+2ax-5a\(^2\)-12ax+6a\(^2\)

=6x\(^2\)+a\(^2\)-25ax

a: \(a^2+6ab+9b^2-1\)

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

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

b: \(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)

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

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

\(=-2\left(2x-5\right)\)

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

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

\(=-5\left(3x-1\right)\left(x+3y\right)\)

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

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

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

e: \(a^2-6a+9-b^2\)

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

\(=\left(a-3-b\right)\left(a-3+b\right)\)

f: \(x^3-y^3-3x^2+3x-1\)

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

\(=\left(x-1\right)^3-y^3\)

\(=\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\)

2x^2 + x - 6

= 2x^2 + 4x - 3x - 6

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

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

7x^2 + 50x + 7 

= 7x^2 + x + 49x + 7

= 7x(x + 7) + x + 7

= (7x + 1)(x + 7)

12x^2 + 7x - 12

15x^2 +  7x - 2

= 15x^2 - 3x + 10x - 2

= 3x(5x - 1) + 2(5x - 1) 

= (3x + 2)(5x - 1)

a^2 - 5a - 14

= a^2 + 2a - 7a - 14

= a(a + 2) - 7(a + 2)

= (a - 7)(a + 2)

2x^2 + 5x + 2

= 2x^2 + x + 4x + 2

= 2x(x + 2) + x + 2

= (2x + 1)(x + 2)

\(2x^2+x-6=2x^2+4x-3x-6\)

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

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

\(7x^2+50x+7\)

\(=7x^2+x+49x+7\)

\(=x\left(7x+1\right)+7\left(7x+1\right)\)

\(=\left(7x+1\right)\left(x+7\right)\)

\(12x^2+7x-12\)

\(=12x^2+16x-9x-12\)

\(=4x\left(3x+4\right)-3\left(3x+4\right)\)

\(=\left(3x+4\right)\left(4x-3\right)\)