9a²-16b² = (3a)²-(4b)²=(3a+4b)(3a-4b)

[ using (a - b)²=a²-2ab+b²]
(2x-3y)² = (2x)²-2(2x)(3y)+(3y)²
= 4x²-12xy+9y²

\(\cfrac { { 25x }^{ 3 }{ y }^{ 2 } }{ -15{ x }^{ 2 }y } =\cfrac { -25 }{ 15 } { x }^{ 3-2 }{ y }^{ 2-1 }=\cfrac { -5 }{ 3 } xy\)

\(\cfrac { -15{ a }^{ 2 }{ bc }^{ 3 } }{ 3ab } =\cfrac { -15 }{ 3 } { a }^{ 2-1 }{ b }^{ 1-1 }{ c }^{ 3 }=-5a{ b }^{ 0 }{ c }^{ 3 }=-5{ ac }^{ 3 }\)

4a\(\times\)3a² = (4\(\times\)3) (a\(\times\)a²) = 12a³

10x² + 15y² 
10x² + 15y² = 5 (2x² + 3y²)
Here, 5 and (2x² + 3y²) are the factors of 10x² + 15y² 

Length of the rectangle = y+ 4
breadth of the rectangle = y - 3
Area of the rectangle = length x breadth
= (y + 4) (y- 3)
=Y + (4 + (-3))y + (4) (-3)
= y² + y - 12

(a²-b²) = (a+b) (a-b)
(3x)²-5² = (3x + 5) (3x - 5)
= 3x(3x - 5) + 5(3x - 5)
= 9x²- 15x + 15x - 25
= 9x² - 25

(a + b)² = a² + 2ab + b²
(100 + 5)²
= (100)² + 2(100)(5) + 5² 
= 10000 + 1000 + 25
105² = 11,025

2y(5x²y − c + 3 d = 10x²y² − 2xy + 6y³
\(10 x^{2} y^{2}-2 y c+6 y d=10 x^{2} y^{2}-2 x y+6 y^{3}\)
Equating the coefficients, we get
- 2yc = 2xy           and      6yd = 6y³
\(c=\frac{-2 x y}{-2 y}\)       and      \(d=\frac{6 y^{3}}{6 y}\)
C = x          and   d = y²

b x (−15m²n³p) = 45m³n³p²
\(\mathrm{b}=\frac{45 m^{3} n^{3} p^{2}}{-15 m^{2} n^{3} p}\)
b = -3mp

6xy x a = −12x³y
\(a=-\frac{12 x y}{6 x y}\)
a = -2x²

= -2mn x (2m)² x -3mn
= -2mn x 4m² x -3mn
= 24m⁴n²

-3x \(\times\) 7y = (-3 \(\times\) 7)(x \(\times\) y) = - 21xy

6x \(\times\) 4= (6 \(\times\) 4)(x) = 24x