Explicación paso a paso:
1)
[tex] {(2x - 4y)}^{2} \\ = {(2x)}^{2} + 2(2x)( - 4y) + {( - 4y)}^{2} \\ = 4 {x}^{2} - 16xy + 16 {y}^{2} [/tex]
2)
[tex] {(3a - 5b)}^{2} \\ = {(3a)}^{2} + 2(3a)( - 5b) + {( - 5b)}^{2} \\ = 9 {a}^{2} - 30ab + 25 {b}^{2} [/tex]
3)
[tex] {(6x - 5y)}^{2} \\ = {(6x)}^{2} + 2(6x)( - 5y) + {( - 5y)}^{2} \\ = 36 {x}^{2} - 60xy + 25 {y}^{2} [/tex]
4)
[tex] {(3x + 2y)}^{2} \\ = {(3x)}^{2} + 2(3x)(2y) + {(2y)}^{2} \\ = 9 {x}^{2} + 12xy + 4 {y}^{2} [/tex]
5)
[tex] {(4pq - 3q)}^{2} \\ = {(4pq)}^{2} + 2(4pq)( - 3q) + {( - 3q)}^{2} \\ = 16 {p}^{2} {q}^{2} - 24pq \: {q}^{2} + 9 {q}^{2} [/tex]
6)
[tex] {(2 {x}^{3} - 5 {y}^{2}) }^{2} \\ = {(2 {x}^{3} )}^{2} + 2(2 {x}^{3} )( - 5 {y}^{2} ) + {( - 5 {y}^{2}) }^{2} \\ = 4 {x}^{6} - 20 {x}^{3} {y}^{2} + 25 {y}^{4} [/tex]
7)
[tex] {(4 {a}^{2} - 3 {b}^{3} ) }^{2} \\ = {(4 {a}^{2} )}^{2} + 2(4 {a}^{2} )( - 3 {b}^{3} ) + {( - {3b}^{3}) }^{2} \\ = 16 {a}^{4} - 24 {a}^{2} {b}^{3} + 9 {b}^{6} [/tex]
8)
[tex] {(4 {x}^{2} + 3 {y}^{3} )}^{2} \\ = {(4 {x}^{2}) }^{2} + 2(4 {x}^{2} )(3 {y}^{3} ) + {(3 {y}^{3}) }^{2} \\ = 16 {x}^{4} + 24 {x}^{2} {y}^{3} + 9 {y}^{6} [/tex]
9)
[tex] {(8 {a}^{2} b + 7a {b}^{6} {y}^{2}) }^{2} \\ = {(8 {a}^{2} b)}^{2} + 2(8 {a}^{2} b)(7a {b}^{6} {y}^{2}) + {(7a {b}^{6} {y}^{2} ) }^{2} \\ = 64 {a}^{4} {b}^{2} + 112 {a}^{3} {b}^{7} {y}^{2} + 49 {a}^{2} {b}^{12} {y}^{4} [/tex]
10)
[tex] {(13ab {x}^{2} + 2ab {y}^{3} )}^{2} \\ = {(13ab {x}^{2} )}^{2} + 2(13ab {x}^{2} )(2ab {y}^{3} ) + {(2ab {y}^{3} )}^{2} \\ = 169 {a}^{2} {b}^{2} {x}^{4} + 52 {a}^{2} {b}^{2} {x}^{2} {y}^{3} + 4 {a}^{2} {b}^{2} {y}^{6} [/tex]
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Explicación paso a paso:
1)
[tex] {(2x - 4y)}^{2} \\ = {(2x)}^{2} + 2(2x)( - 4y) + {( - 4y)}^{2} \\ = 4 {x}^{2} - 16xy + 16 {y}^{2} [/tex]
2)
[tex] {(3a - 5b)}^{2} \\ = {(3a)}^{2} + 2(3a)( - 5b) + {( - 5b)}^{2} \\ = 9 {a}^{2} - 30ab + 25 {b}^{2} [/tex]
3)
[tex] {(6x - 5y)}^{2} \\ = {(6x)}^{2} + 2(6x)( - 5y) + {( - 5y)}^{2} \\ = 36 {x}^{2} - 60xy + 25 {y}^{2} [/tex]
4)
[tex] {(3x + 2y)}^{2} \\ = {(3x)}^{2} + 2(3x)(2y) + {(2y)}^{2} \\ = 9 {x}^{2} + 12xy + 4 {y}^{2} [/tex]
5)
[tex] {(4pq - 3q)}^{2} \\ = {(4pq)}^{2} + 2(4pq)( - 3q) + {( - 3q)}^{2} \\ = 16 {p}^{2} {q}^{2} - 24pq \: {q}^{2} + 9 {q}^{2} [/tex]
6)
[tex] {(2 {x}^{3} - 5 {y}^{2}) }^{2} \\ = {(2 {x}^{3} )}^{2} + 2(2 {x}^{3} )( - 5 {y}^{2} ) + {( - 5 {y}^{2}) }^{2} \\ = 4 {x}^{6} - 20 {x}^{3} {y}^{2} + 25 {y}^{4} [/tex]
7)
[tex] {(4 {a}^{2} - 3 {b}^{3} ) }^{2} \\ = {(4 {a}^{2} )}^{2} + 2(4 {a}^{2} )( - 3 {b}^{3} ) + {( - {3b}^{3}) }^{2} \\ = 16 {a}^{4} - 24 {a}^{2} {b}^{3} + 9 {b}^{6} [/tex]
8)
[tex] {(4 {x}^{2} + 3 {y}^{3} )}^{2} \\ = {(4 {x}^{2}) }^{2} + 2(4 {x}^{2} )(3 {y}^{3} ) + {(3 {y}^{3}) }^{2} \\ = 16 {x}^{4} + 24 {x}^{2} {y}^{3} + 9 {y}^{6} [/tex]
9)
[tex] {(8 {a}^{2} b + 7a {b}^{6} {y}^{2}) }^{2} \\ = {(8 {a}^{2} b)}^{2} + 2(8 {a}^{2} b)(7a {b}^{6} {y}^{2}) + {(7a {b}^{6} {y}^{2} ) }^{2} \\ = 64 {a}^{4} {b}^{2} + 112 {a}^{3} {b}^{7} {y}^{2} + 49 {a}^{2} {b}^{12} {y}^{4} [/tex]
10)
[tex] {(13ab {x}^{2} + 2ab {y}^{3} )}^{2} \\ = {(13ab {x}^{2} )}^{2} + 2(13ab {x}^{2} )(2ab {y}^{3} ) + {(2ab {y}^{3} )}^{2} \\ = 169 {a}^{2} {b}^{2} {x}^{4} + 52 {a}^{2} {b}^{2} {x}^{2} {y}^{3} + 4 {a}^{2} {b}^{2} {y}^{6} [/tex]