(b) Factorise: \( \begin{array}{llll}\text { (1) } & x(a+b)+y(a+b) & \text { (2) } & k(x+y)+p(x+y) \\ \text { (3) } & 3 p(q+r)-4 m(r+q) & \text { (4) } & 7 k(m-3 n)-3 p(m-3 n) \\ \text { (5) } & (x-y)^{2}-3(x-y) & \text { (6) } & (a+c)^{4}+(a+c)^{5} \\ \text { (7) } & (m-n)^{6}+(m-n)^{2} & \text { (8) } & 7 x(m-3 n)-4 y(3 n-m) \\ \text { (9) } & 7 x(m-3 n)+4 y(3 n-m) & \text { (10) } & 7 x(m+3 n)+4 y(-m-3 n) \\ \text { (11) } & 2 x(3 p+q)+4 y(-q-3 p) & \text { (12) } & (a-b)-(p b-p a) \\ \text { (13) } & 4 x\left(a^{3}-2\right)+\left(2-a^{3}\right) & \text { (14) } & 2 x^{2}(3 a-b)-12 x(b-3 a) \\ \text { (15) } & (a-3 b)-c(3 b-a)+d(3 b-a)\end{array} \)
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Mind Expander
1) The expressions can be factored in elegant ways by recognizing common terms or patterns. For example, in the first expression \(x(a+b) + y(a+b)\), we notice that \(a+b\) is a shared factor, allowing us to factor it out: \((a+b)(x+y)\). Similarly, for \((x-y)^{2}-3(x-y)\), we can see that \((x-y)\) is common, leading to \((x-y)((x-y)-3)\) as the factored form. 2) Understanding the principles of factoring is not just about making your math homework easier—it’s a powerful tool in real-world applications such as simplifying expressions in coding, engineering calculations, or even financial modeling! Factoring helps simplify complex problems and makes computations less prone to error. Imagine trying to budget for a party; if you factor your expenses properly, it becomes far easier to manage costs and stay within your limit!
