Factorise: (1) \( \quad x(a+b)+y(a+b) \) (3) \( 3 p(q+r)-4 m(r+q) \) (5) \( (x-y)^{2}-3(x-y) \)

Sure, let's factor each of the given expressions step by step. --- ### **(1) \( x(a + b) + y(a + b) \)** **Step 1:** Identify the common factor in both terms. - Both terms have \((a + b)\) as a common factor. **Step 2:** Factor out \((a + b)\). \[ x(a + b) + y(a + b) = (a + b)(x + y) \] **Factored Form:** \[ (a + b)(x + y) \] --- ### **(3) \( 3p(q + r) - 4m(q + r) \)** **Step 1:** Identify the common factor in both terms. - Both terms have \((q + r)\) as a common factor. **Step 2:** Factor out \((q + r)\). \[ 3p(q + r) - 4m(q + r) = (q + r)(3p - 4m) \] **Factored Form:** \[ (q + r)(3p - 4m) \] --- ### **(5) \( (x - y)^2 - 3(x - y) \)** **Step 1:** Let’s substitute \( u = (x - y) \) to simplify the expression. \[ u^2 - 3u \] **Step 2:** Factor out the common term \( u \). \[ u(u - 3) \] **Step 3:** Substitute back \( u = (x - y) \). \[ (x - y)(x - y - 3) \] **Factored Form:** \[ (x - y)(x - y - 3) \] --- **Summary of Factored Forms:** 1. \( (a + b)(x + y) \) 2. \( (q + r)(3p - 4m) \) 3. \( (x - y)(x - y - 3) \)