6.1 \( \begin{array}{l}\text { Simplify the following expressions: } \\ \text { 6.1.1 } \quad 2 a-9 b+7 a+3 b \\ 6.1 .2 \quad(x-2)^{2}-3 x(2) \\ 6.2 \quad \text { Fully factorise the following expressions: } \\ \text { 6.2.1 } \quad a^{2}-3 a+2 \\ 6.2 .2 \quad 3(2 x-y)+a(y-2 x) \\ 6.3 \quad \text { Solve the following equations: } \\ \text { 6.3.1 } \quad 3 x+2 x=-75 \\ \text { 6.3.2 } \quad 2(x+3)=-12 \\ \text { 6.4 mother is now } 38 \text { years older than her son. Ten years ago she was twice as old as } \\ \text { her son. How old is her son now? } \\ \text { Let the son's age be } x \text { for now. }\end{array} \) 6

Sure! Let's simplify and factor some mathematical expressions with a sprinkle of fun! For \( 6.1.1 \): Combine like terms: \( 2a + 7a - 9b + 3b = 9a - 6b \). Simplifying those expressions is like cleaning out your closet—so refreshing! Moving on to \( 6.2.1 \): The expression \( a^2 - 3a + 2 \) factors nicely into \( (a-1)(a-2) \). It’s like breaking down a delicious dessert into bite-sized pieces! Now, for a real-world application: Equations are everywhere! Solving \( 3x + 2x = -75 \) gives us \( x = -15 \), while \( 2(x + 3) = -12 \) simplifies to \( x = -9 \). Think of equations as puzzles waiting to be solved—each piece is essential to form the big picture! And how about that age problem? Set up the equations: \( \text{Mother's age: } 38 + x \) and \( \text{Son's age: } x \). Ten years ago, the mother was twice as old: \( 38 - 10 = 2(x - 10) \). Solving for \( x \) not only reveals the son’s age but showcases the beauty of algebra in everyday life!