Đáp án:
\(\eqalign{
& a)\,1062 \cr
& b)\, - 8912 \cr
& c)\,29 \cr} \)
Giải thích các bước giải:
\(\eqalign{
& Bai\,\,3 \cr
& a)\,\,5{\left( {x + 4} \right)^2} + 4{\left( {x + 5} \right)^2} - 9\left( {4 + x} \right)\left( {x - 4} \right) - \left( {x - 1} \right)\left( {2x + 3} \right) \cr
& = 5\left( {{x^2} + 8x + 16} \right) + 4\left( {{x^2} + 10x + 25} \right) - 9\left( {{x^2} - 16} \right) - \left( {2{x^2} + 3x - 2x - 3} \right) \cr
& = 5{x^2} + 40x + 80 + 4{x^2} + 40x + 100 - 9{x^2} + 144 - 2{x^2} - x + 3 \cr
& = - 2{x^2} + 79x + 327 \cr
& Thay\,\,x = 15 \cr
& \Rightarrow - {2.15^2} + 79.15 + 327 = 1062 \cr
& b)\,\,{\left( {x - 2} \right)^3} - \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) + 6\left( {x - 2} \right)\left( {x + 2} \right) - x\left( {x - 1} \right) \cr
& = {x^3} - 6{x^2} + 12x - 8 - \left( {{x^3} - 8} \right) + 6\left( {{x^2} - 4} \right) - {x^2} + x \cr
& = {x^3} - 6{x^2} + 12x - 8 - {x^3} + 8 + 6{x^2} - 24 - {x^2} + x \cr
& = - {x^2} + 13x - 24 \cr
& Thay\,\,x = 101 \cr
& \Rightarrow - {101^2} + 13.101 - 24 = - 8912 \cr
& c)\,\,{\left( {x - 1} \right)^3} - \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) + 3{\left( {2x - 1} \right)^2} \cr
& = {x^3} - 3{x^2} + 3x - 1 - \left( {{x^3} + 27} \right) + 3\left( {4{x^2} - 4x + 1} \right) \cr
& = {x^3} - 3{x^2} + 3x - 1 - {x^3} - 27 + 12{x^2} - 12x + 3 \cr
& = 9{x^2} - 9x - 25 \cr
& Thay\,\,x = - 2 \cr
& \Rightarrow 9{\left( { - 2} \right)^2} - 9\left( { - 2} \right) - 25 = 29 \cr} \)
