1. **Problem statement:** We are asked to rewrite and reduce algebraic expressions using the square formulas (kvadratsætningerne). 2. **Square formulas used:** - First square formula: $ (a+b)^2 = a^2 + 2ab + b^2 $ - Second square formula: $ (a-b)^2 = a^2 - 2ab + b^2 $ - Third formula (difference of squares): $ (a+b)(a-b) = a^2 - b^2 $ 3. **Step-by-step solutions for Opgave 1:** **1) $(x + y)^2$** $$ (x + y)^2 = x^2 + 2xy + y^2 $$ **2) $(3x + 4y)^2$** $$ (3x + 4y)^2 = (3x)^2 + 2 \cdot 3x \cdot 4y + (4y)^2 = 9x^2 + 24xy + 16y^2 $$ **3) $(8 + 2a)^2$** $$ (8 + 2a)^2 = 8^2 + 2 \cdot 8 \cdot 2a + (2a)^2 = 64 + 32a + 4a^2 $$ **4) $(n - m)^2$** $$ (n - m)^2 = n^2 - 2nm + m^2 $$ **5) $(5x - y)^2$** $$ (5x - y)^2 = (5x)^2 - 2 \cdot 5x \cdot y + y^2 = 25x^2 - 10xy + y^2 $$ **6) $(10 - 4g)^2$** $$ (10 - 4g)^2 = 10^2 - 2 \cdot 10 \cdot 4g + (4g)^2 = 100 - 80g + 16g^2 $$ **7) $(x + y)(x - y)$** $$ (x + y)(x - y) = x^2 - y^2 $$ **8) $(4a + b)(4a - b)$** $$ (4a + b)(4a - b) = (4a)^2 - b^2 = 16a^2 - b^2 $$ **9) $(10x + 5y)(10x - 5y)$** $$ (10x + 5y)(10x - 5y) = (10x)^2 - (5y)^2 = 100x^2 - 25y^2 $$ 4. **Summary:** Each expression is rewritten by applying the appropriate square formula or difference of squares formula, expanding and simplifying step-by-step.