2. Simplify each of the following expressions:(i) (3+3)(2+2)(ii) (3+3)(3−3)(iii) (5+2)2(iv) (5−2)(5+2)Recall, π is defined as the ratio of the circumference (syy) of a circ
Q. 2. Simplify each of the following expressions:(i) (3+3)(2+2)(ii) (3+3)(3−3)(iii) (5+2)2(iv) (5−2)(5+2)Recall, π is defined as the ratio of the circumference (syy) of a circ
Distribute and Multiply: (i) Multiply (3+3)(2+2) using the distributive property.(3+3)(2+2)=3×2+3×2+3×2+3×2=6+32+23+6
Difference of Squares: (ii) Multiply (3+3)(3−3) using the difference of squares formula.(3+\sqrt{3})(3-\sqrt{3}) = 3^2 - (\sqrt{3})^2\(\newline= 9 - 3= 6\)
Square Formula: (iii) Square (5+2) using the formula (a+b)2=a2+2ab+b2.(\sqrt{5}+\sqrt{2})^2 = (\sqrt{5})^2 + 2\cdot\sqrt{5}\cdot\sqrt{2} + (\sqrt{2})^2\(\newline= 5 + 2\sqrt{10} + 2= 7 + 2\sqrt{10}\)
Difference of Squares: (iv) Multiply (5−2)(5+2) using the difference of squares formula.(\sqrt{\(5\)}-\sqrt{\(2\)})(\sqrt{\(5\)}+\sqrt{\(2\)}) = (\sqrt{\(5\)})^\(2 - (\sqrt{2})^2= 5 - 2= 3
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