Question

por favor alguém me ajuda, é urgente!!


complete as expressões com o termo que esta faltando para que seja trinomios quadrados perfeitos :

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Answer 1

$\boxed{\begin{array}{l}\sf (a+b)^2=a^2+2ab+b^2\\\sf (a-b)^2=a^2-2ab+b^2\\\tt a) 16x^2+\boxed{}+100=a^2+2ab+b^2\\\sf a^2=16x^2\implies a=4x\\\sf b^2=100\implies b=10\\\sf 2ab=2\cdot4x\cdot10=80x\\\sf 16x^2+\boxed{\sf80x}+100\end{array}}$

$\boxed{\begin{array}{l}\tt b)~\sf81x^2-\boxed{}+1\\\sf a^2=81x^2\implies a=9x\\\sf b^2=1\implies b=1\\\sf 2ab=2\cdot9x\cdot1=18x\\\sf 81x^2-\boxed{\sf18x}+1\end{array}}$

$\boxed{\begin{array}{l}\tt c)~\sf169y^2+\boxed{}+z^2\\\sf a^2=169y^2\implies a=13y\\\sf b^2=z^2\implies b=z\\\sf 2ab=2\cdot13y\cdot z=26yz\\\sf 169y^2+\boxed{\sf26yz}+z^2\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf a^2-\boxed{}+256\\\sf a^2=a^2\implies a=a\\\sf b^2=256\implies b=16\\\sf2ab=2\cdot a\cdot16=32a\\\sf a^2-\boxed{\sf32a}+256\end{array}}$