common bracket. Eydercise 1: Factorise a) \( m y+5 n y+m x+5 n x \) c) \( 3 p x+6 p y+2 q x+4 q y \) e) \( 16-x^{2}-4 y+x y \) g) \( x^{2}-x^{2}+x+y \) i) \( 10 x^{2}+5 x y+6 x y+3 y^{2} \) k) \( 27 a^{2} x-12 b^{2} x-18 a^{2} y+8 b^{2} y \) m) \( 16 x^{2}-9 y^{2}+(4 x-3 y)(x+2 y \) o) \( 5 p^{2}-2 q-5 q^{2}+2 p \) in

Factor the expression by following steps: - step0: Factor: \(3px+6py+2qx+4qy\) - step1: Factor the expression: \(3p\left(x+2y\right)+2q\left(x+2y\right)\) - step2: Factor the expression: \(\left(3p+2q\right)\left(x+2y\right)\) Factor the expression \( m y+5 n y+m x+5 n x \). Factor the expression by following steps: - step0: Factor: \(my+5ny+mx+5nx\) - step1: Rewrite the expression: \(my+mx+5ny+5nx\) - step2: Factor the expression: \(m\left(y+x\right)+5n\left(y+x\right)\) - step3: Factor the expression: \(\left(m+5n\right)\left(y+x\right)\) Factor the expression \( 16-x^{2}-4 y+x y \). Factor the expression by following steps: - step0: Factor: \(16-x^{2}-4y+xy\) - step1: Rewrite the expression: \(-x^{2}+4x+yx-4y-4x+16\) - step2: Factor the expression: \(-x\left(x-4\right)+y\left(x-4\right)-4\left(x-4\right)\) - step3: Factor the expression: \(\left(-x+y-4\right)\left(x-4\right)\) - step4: Factor the expression: \(-\left(x-y+4\right)\left(x-4\right)\) Factor the expression \( 5 p^{2}-2 q-5 q^{2}+2 p \). Factor the expression by following steps: - step0: Factor: \(5p^{2}-2q-5q^{2}+2p\) - step1: Rewrite the expression: \(5p^{2}-5pq+5qp-5q^{2}+2p-2q\) - step2: Factor the expression: \(5p\left(p-q\right)+5q\left(p-q\right)+2\left(p-q\right)\) - step3: Factor the expression: \(\left(5p+5q+2\right)\left(p-q\right)\) Factor the expression \( 10 x^{2}+5 x y+6 x y+3 y^{2 \). Factor the expression by following steps: - step0: Factor: \(10x^{2}+5xy+6xy+3y^{2}\) - step1: Add the terms: \(10x^{2}+11xy+3y^{2}\) - step2: Rewrite the expression: \(10x^{2}+\left(5+6\right)xy+3y^{2}\) - step3: Rewrite the expression: \(10x^{2}+5xy+6yx+3y^{2}\) - step4: Factor the expression: \(5x\left(2x+y\right)+3y\left(2x+y\right)\) - step5: Factor the expression: \(\left(5x+3y\right)\left(2x+y\right)\) Factor the expression \( 27 a^{2} x-12 b^{2} x-18 a^{2} y+8 b^{2} y \). Factor the expression by following steps: - step0: Factor: \(27a^{2}x-12b^{2}x-18a^{2}y+8b^{2}y\) - step1: Rewrite the expression: \(27a^{2}x-18a^{2}y-12b^{2}x+8b^{2}y\) - step2: Factor the expression: \(9a^{2}\left(3x-2y\right)-4b^{2}\left(3x-2y\right)\) - step3: Factor the expression: \(\left(9a^{2}-4b^{2}\right)\left(3x-2y\right)\) - step4: Factor the expression: \(\left(3a+2b\right)\left(3a-2b\right)\left(3x-2y\right)\) Factor the expression \( 16 x^{2}-9 y^{2}+(4 x-3 y)(x+2 y) \). Factor the expression by following steps: - step0: Factor: \(16x^{2}-9y^{2}+\left(4x-3y\right)\left(x+2y\right)\) - step1: Factor the expression: \(\left(4x+3y+x+2y\right)\left(4x-3y\right)\) - step2: Factor the expression: \(5\left(x+y\right)\left(4x-3y\right)\) Here are the factorizations for the given expressions: a) \( m y + 5 n y + m x + 5 n x \) To factor this expression, we can group the terms: \[ = (m + 5n)(y + x) \] --- c) \( 3 p x + 6 p y + 2 q x + 4 q y \) We can factor by grouping: \[ = (3p + 2q)(x + 2y) \] --- e) \( 16 - x^{2} - 4y + x y \) Rearranging and factoring gives: \[ = -(x - y + 4)(x - 4) \] --- g) \( x^{2} - x^{2} + x + y \) This simplifies to: \[ = x + y \] However, it cannot be factored further since it is already in its simplest form. --- i) \( 10 x^{2} + 5 x y + 6 x y + 3 y^{2} \) Combining like terms and factoring gives: \[ = (5x + 3y)(2x + y) \] --- k) \( 27 a^{2} x - 12 b^{2} x - 18 a^{2} y + 8 b^{2} y \) Factoring by grouping results in: \[ = (3a + 2b)(3a - 2b)(3x - 2y) \] --- m) \( 16 x^{2} - 9 y^{2} + (4 x - 3 y)(x + 2 y) \) This can be factored as: \[ = 5(x + y)(4x - 3y) \] --- o) \( 5 p^{2} - 2 q - 5 q^{2} + 2 p \) Rearranging and factoring gives: \[ = (5p + 5q + 2)(p - q) \] --- If you have any further questions or need additional assistance, feel free to ask!