Resposta:

[tex]\sf{segue \: abaixo \: a \: resposta}[/tex]

Explicação passo-a-passo:

a)

[tex]\sf{(a+13)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax13 + {13}^{2} }[/tex]

[tex]\sf{2x13 = 26}[/tex]

[tex]\sf{ {a}^{2} + 26a + {13}^{2} }[/tex]

[tex]\sf{ {13}^{2} = 13x3 = 169 }[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 26a + 169 }}}}[/tex]

b)

[tex]\sf{(a+14)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax14 + {14}^{2} }[/tex]

[tex]\sf{2x14 = 28}[/tex]

[tex]\sf{ {a}^{2} + 28a + {14}^{2} }[/tex]

[tex]\sf{ {14}^{2} = 14x14 = 196}[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 28a + 196}}}}[/tex]

c)

[tex]\sf{(a+15)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax15 + {15}^{2} }[/tex]

[tex]\sf{2x15 = 30}[/tex]

[tex]\sf{ {a}^{2} + 30a + {15}^{2} }[/tex]

[tex]\sf{ {15}^{2} = 15x15 = 225 }[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 30a + 225 }}}}[/tex]

d)

[tex]\sf{(a+16)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax16 + {16}^{2} }[/tex]

[tex]\sf{2x16 = 32}[/tex]

[tex]\sf{ {a}^{2} + 32a + {16}^{2} }[/tex]

[tex]\sf{ {16}^{2} = 16x16 = 256}[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 32a + 256}}}}[/tex]

e)

[tex]\sf{(a+17)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax17 + {17}^{2} }[/tex]

[tex]\sf{2x17 = 34}[/tex]

[tex]\sf{ {a}^{2} + 34a + {17}^{2} }[/tex]

[tex]\sf{ {17}^{2} = 17x17 = 289}[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 34a + 289}}}}[/tex]

f)

[tex]\sf{(a+18)²}[/tex]

[tex]\sf{ {a}^{2} + 2ax18 + {18}^{2} }[/tex]

[tex]\sf{2x18 = 36}[/tex]

[tex]\sf{ {a}^{2} + 36a + {18}^{2} }[/tex]

[tex]\sf{ {18}^{2} = 18x18 = 324}[/tex]

[tex]\boxed{\boxed{{\sf{ {a}^{2} + 36a + 324}}}}[/tex]

Explicação passo-a-passo:

[tex]a)(a + 13) {}^{2} = a {}^{2} + 2.a.13 + 13 {}^{2} = a {}^{2} + 26a + 169[/tex]

[tex]b)(a + 14) {}^{2} = a {}^{2} + 2.14.a + 14 {}^{2} = a {}^{2} + 28a + 196[/tex]

[tex]c)(a + 15) {}^{2} = a {}^{2} + 2.15.a + 15 {}^{2} = a {}^{2} + 30a + 225[/tex]

[tex]d)(a + 16) {}^{2} = a {}^{2} + 2.16.a + 16 {}^{2} = a {}^{2} + 32a + 256[/tex]

[tex]e)(a + 17) {}^{2} = a {}^{2} + 2.17a + 17 {}^{2} = a {}^{2} + 34a + 289[/tex]

[tex]f)(a + 1) {}^{2} = a {}^{2} + 2.18.a + 18 {}^{2} = a {}^{2} + 36a + 324[/tex]