Explicație pas cu pas:
[tex]a)( - 13a + 26 {a}^{2} - 39 {a}^{3} ) \div ( - 13a) - (12 \sqrt{3} {a}^{4} - 6 \sqrt{3} {a}^{5} ) \div {( - \sqrt{3} a)}^{3} = \\ 1 - 2a + 3 {a}^{2} - (12 \sqrt{3} {a}^{4} - 6 \sqrt{3} {a}^{5} ) \div( ( - { \sqrt{3} )}^{3} \times {a}^{3}) ) \\ = 1 - 2a + 3 {a}^{2} - (12 \sqrt{3} {a}^{4} - 6 \sqrt{3} {a}^{5} ) \div ( - 3 \sqrt{3} {a}^{3} ) \\ = 1 - 2a + 3 {a}^{2} - ( - 4a + 2 {a}^{2} ) \\ = 1 - 2a + 3 {a}^{2} + 4a - 2 {a}^{2} = {a}^{2} + 2a + 1 = {(a + 1)}^{2} [/tex]
[tex]b)(( {3 \sqrt{2}a) }^{4} - {(2 \sqrt{3} {a}^{2} )}^{2} ) \div (4a) - 70 {a}^{5} {b}^{2} \div {( \sqrt{10}ab) }^{2} + ( - {3a)}^{3} = \\ = ( {(3 \sqrt{2}) }^{4} \times {a}^{4} ) - ( {(2 \sqrt{3}) }^{2} \times {a}^{4} ) \div (4a) - 70 {a}^{5} {b}^{2} \div ( { \sqrt{10} }^{2} {a}^{2} {b}^{2} ) - {3}^{3} {a}^{3} = \\ = (324 {a}^{4} - 12 {a}^{4} ) \div (4a) - 70 {a}^{5} {b}^{2} \div (10 {a}^{2} {b}^{2} ) - 27 {a}^{3} = \\ = 312 {a}^{4} \div (4a) - 7 {a}^{3} - 27 {a}^{3} = \\ = 78 {a}^{3} - 7 {a}^{3} - 27 {a}^{3} = 71 {a}^{3} - 27 {a}^{3} = 44 {a}^{3} [/tex]
