Представьте в виде многочлена квадрат двучлена:
а) ( − 9 a + 4 b ) 2 ; {\displaystyle (-9a+4b)^{2};} б) ( − 11 x − 7 y ) 2 ; {\displaystyle (-11x-7y)^{2};} в) ( − 0 , 8 x − 0 , 5 b ) 2 ; {\displaystyle (-0,8x-0,5b)^{2};} г) ( − 1 1 3 p + 6 q ) 2 ; {\displaystyle \left(-1{\frac {1}{3}}p+6q\right)^{2};} д) ( 0 , 08 a − 50 b ) 2 ; {\displaystyle (0,08a-50b)^{2};} е) ( − 0 , 5 x − 60 y ) 2 ; {\displaystyle (-0,5x-60y)^{2};}
а) ( − 9 a + 4 b ) 2 = ( 4 b − 9 a ) 2 = ( 4 b ) 2 − 2 ⋅ 4 b ⋅ 9 a + ( 9 a ) 2 = 16 b 2 − 72 a b + 81 a 2 {\displaystyle (-9a+4b)^{2}=(4b-9a)^{2}=(4b)^{2}-2\cdot 4b\cdot 9a+(9a)^{2}=16b^{2}-72ab+81a^{2}} б) ( − 11 x − 7 y ) 2 = ( − ( 11 x + 7 y ) ) 2 = ( 11 x + 7 y ) 2 = ( 11 x ) 2 + 2 ⋅ 11 x ⋅ 7 y + ( 7 y ) 2 = 121 x 2 + 154 x + 4 x 2 {\displaystyle (-11x-7y)^{2}=(-(11x+7y))^{2}=(11x+7y)^{2}=(11x)^{2}+2\cdot 11x\cdot 7y+(7y)^{2}=121x^{2}+154x+4x^{2}} в) ( − 0 , 8 x − 0 , 5 b ) 2 = ( − ( 0 , 8 x + 0 , 5 b ) ) 2 = ( 0.8 x + 0 , 5 b ) 2 == ( 0 , 8 x ) 2 + 2 ⋅ 0 , 8 x ⋅ 0 , 5 b + ( 0 , 5 b ) 2 = 0 , 64 x 2 + 0 , 8 b x + 0 , 25 b 2 {\displaystyle (-0,8x-0,5b)^{2}=(-(0,8x+0,5b))^{2}=(0.8x+0,5b)^{2}==(0,8x)^{2}+2\cdot 0,8x\cdot 0,5b+(0,5b)^{2}=0,64x^{2}+0,8bx+0,25b^{2}} г) ( − 1 1 3 p + 6 q ) 2 = ( 6 q − 1 1 3 p ) 2 = ( 6 q ) 2 − 2 ⋅ 6 q ⋅ 4 3 p + ( 4 3 p ) 2 = 36 q 2 − 16 p q + 16 9 p 2 {\displaystyle \left(-1{\frac {1}{3}}p+6q\right)^{2}=\left(6q-1{\frac {1}{3}}p\right)^{2}=(6q)^{2}-2\cdot 6q\cdot {\frac {4}{3}}p+\left({\frac {4}{3}}p\right)^{2}=36q^{2}-16pq+{\frac {16}{9}}p^{2}} д) ( 0 , 08 a − 50 b ) 2 = ( 0 , 08 a ) 2 − 2 ⋅ 0 , 8 a ⋅ 5 b + ( 50 b ) 2 = 0 , 0064 a 2 − 8 a b + 2500 b 2 {\displaystyle (0,08a-50b)^{2}=(0,08a)^{2}-2\cdot 0,8a\cdot 5b+(50b)^{2}=0,0064a^{2}-8ab+2500b^{2}} е) ( − 0 , 5 x − 60 y ) 2 = ( − ( 0 , 5 x + 60 y ) ) 2 = ( 0 , 5 x + 60 y ) 2 = ( 0 , 5 x ) 2 + 2 ⋅ 0 , 5 x ⋅ 60 y + ( 60 y ) 2 = 025 x 2 + 60 x y + 3600 y 2 {\displaystyle (-0,5x-60y)^{2}=(-(0,5x+60y))^{2}=(0,5x+60y)^{2}=(0,5x)^{2}+2\cdot 0,5x\cdot 60y+(60y)^{2}=025x^{2}+60xy+3600y^{2}}
