Factorise the following expressions: (1) \( m x+m y+n x+n y \) (3) \( 3 a p-3 b p-3 a q+3 b q \) (5) \( 2 x^{3}-8 x y^{2}+x^{2} y-4 y^{3} \) (7) \( p x^{3}+p+x^{3}+1 \) (9) \( x y+3 a+3 y+a x \) (11) \( a^{2} x+y-x-a^{2} y \)

Factor the expression \( m*x+m*y+n*x+n*y \). Factor the expression by following steps: - step0: Factor: \(mx+my+nx+ny\) - step1: Factor the expression: \(m\left(x+y\right)+n\left(x+y\right)\) - step2: Factor the expression: \(\left(m+n\right)\left(x+y\right)\) Factor the expression \( 3*a*p-3*b*p-3*a*q+3*b*q \). Factor the expression by following steps: - step0: Factor: \(3ap-3bp-3aq+3bq\) - step1: Factor the expression: \(3\left(ap-aq-bp+bq\right)\) - step2: Factor the expression: \(3\left(a\left(p-q\right)-b\left(p-q\right)\right)\) - step3: Factor the expression: \(3\left(a-b\right)\left(p-q\right)\) Factor the expression \( 2*x^3-8*x*y^2+x^2*y-4*y^3 \). Factor the expression by following steps: - step0: Factor: \(2x^{3}-8xy^{2}+x^{2}y-4y^{3}\) - step1: Rewrite the expression: \(2x^{3}-8xy^{2}+yx^{2}-4y^{3}\) - step2: Factor the expression: \(2x\left(x^{2}-4y^{2}\right)+y\left(x^{2}-4y^{2}\right)\) - step3: Factor the expression: \(\left(2x+y\right)\left(x^{2}-4y^{2}\right)\) - step4: Factor the expression: \(\left(2x+y\right)\left(x+2y\right)\left(x-2y\right)\) Factor the expression \( p*x^3+p+x^3+1 \). Factor the expression by following steps: - step0: Factor: \(px^{3}+p+x^{3}+1\) - step1: Evaluate: \(x^{3}p+x^{3}+p+1\) - step2: Rewrite the expression: \(x^{3}p+x^{3}+x^{2}p+x^{2}-x^{2}p-x^{2}-xp-x+xp+x+p+1\) - step3: Factor the expression: \(x^{2}\left(xp+x+p+1\right)-x\left(xp+x+p+1\right)+xp+x+p+1\) - step4: Factor the expression: \(\left(x^{2}-x+1\right)\left(xp+x+p+1\right)\) - step5: Factor the expression: \(\left(x^{2}-x+1\right)\left(x+1\right)\left(p+1\right)\) Factor the expression \( x*y+3*a+3*y+a*x \). Factor the expression by following steps: - step0: Factor: \(xy+3a+3y+ax\) - step1: Rewrite the expression: \(xy+xa+3y+3a\) - step2: Factor the expression: \(x\left(y+a\right)+3\left(y+a\right)\) - step3: Factor the expression: \(\left(x+3\right)\left(y+a\right)\) Factor the expression \( a^2*x+y-x-a^2*y \). Factor the expression by following steps: - step0: Factor: \(a^{2}x+y-x-a^{2}y\) - step1: Rewrite the expression: \(a^{2}x-a^{2}y-x+y\) - step2: Factor the expression: \(a^{2}\left(x-y\right)-\left(x-y\right)\) - step3: Factor the expression: \(\left(a^{2}-1\right)\left(x-y\right)\) - step4: Factor the expression: \(\left(a+1\right)\left(a-1\right)\left(x-y\right)\) The factored forms of the given expressions are: 1. \( m x+m y+n x+n y = (m+n)(x+y) \) 2. \( 3 a p-3 b p-3 a q+3 b q = 3(a-b)(p-q) \) 3. \( 2 x^{3}-8 x y^{2}+x^{2} y-4 y^{3} = (2x+y)(x+2y)(x-2y) \) 4. \( p x^{3}+p+x^{3}+1 = (x^{2}-x+1)(x+1)(p+1) \) 5. \( x y+3 a+3 y+a x = (x+3)(y+a) \) 6. \( a^{2} x+y-x-a^{2} y = (a+1)(a-1)(x-y) \)