Binomial Squares 8B287D

1. **Problem statement:** Decompose each expression as a perfect square trinomial. 2. **Formula used:** For any binomial $(A \pm B)^2 = A^2 \pm 2AB + B^2$. --- ### a) $(12x^2 - 0,3)^2$ 3. Identify $A = 12x^2$, $B = 0.3$. 4. Apply formula: $$ (12x^2)^2 - 2 \times 12x^2 \times 0.3 + (0.3)^2 = 144x^4 - 7.2x^2 + 0.09 $$ --- ### n) $(2x^2 - 3y)^2$ 5. Identify $A = 2x^2$, $B = 3y$. 6. Apply formula: $$ (2x^2)^2 - 2 \times 2x^2 \times 3y + (3y)^2 = 4x^4 - 12x^2y + 9y^2 $$ --- ### m) $(3a^3b - 4m)^2$ 7. Identify $A = 3a^3b$, $B = 4m$. 8. Apply formula: $$ (3a^3b)^2 - 2 \times 3a^3b \times 4m + (4m)^2 = 9a^6b^2 - 24a^3bm + 16m^2 $$ --- ### q) $(2x^{11} + 9x^8)^2$ 9. Identify $A = 2x^{11}$, $B = 9x^8$. 10. Apply formula: $$ (2x^{11})^2 + 2 \times 2x^{11} \times 9x^8 + (9x^8)^2 = 4x^{22} + 36x^{19} + 81x^{16} $$ --- ### w) $[m(C3) - h]^2$ 11. Identify $A = m(C3)$, $B = h$. 12. Apply formula: $$ (m(C3))^2 - 2 \times m(C3) \times h + h^2 = m^2(C3)^2 - 2m(C3)h + h^2 $$ --- **Final answers:** - a) $144x^4 - 7.2x^2 + 0.09$ - n) $4x^4 - 12x^2y + 9y^2$ - m) $9a^6b^2 - 24a^3bm + 16m^2$ - q) $4x^{22} + 36x^{19} + 81x^{16}$ - w) $m^2(C3)^2 - 2m(C3)h + h^2$