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Complete the following procedure to obtain the perfect square trinomial:

[tex]\((5x + 8y)\)[/tex]

The square of the sum of the terms is equal to:

a) The square of the first term:
[tex]\[ (5x)^2 \][/tex]

b) Plus twice the product of both terms:
[tex]\[ 2 \times (5x) \times (8y) \][/tex]

c) Plus the square of the second term:
[tex]\[ (8y)^2 \][/tex]

Sagot :

GinnyAnsweridn
Para completar el trinomio cuadrado perfecto del binomio [tex]\((5x + 8y)\)[/tex] debemos seguir estos pasos.

1. El cuadrado del primer término:

Considera el primer término del binomio, que es [tex]\(5x\)[/tex].

[tex]\[ (5x)^2 = 25x^2 \][/tex]

2. El doble del producto de ambos términos:

Tomamos ambos términos del binomio, que son [tex]\(5x\)[/tex] y [tex]\(8y\)[/tex], y los multiplicamos, luego multiplicamos el resultado por 2:

[tex]\[ 2(5x \cdot 8y) = 2(40xy) = 80xy \][/tex]

3. El cuadrado del segundo término:

Considera el segundo término del binomio, que es [tex]\(8y\)[/tex].

[tex]\[ (8y)^2 = 64y^2 \][/tex]

Por lo tanto, el trinomio cuadrado perfecto resultante del binomio [tex]\((5x + 8y)\)[/tex] será la suma de los tres términos calculados:

[tex]\[ (5x + 8y)^2 = 25x^2 + 80xy + 64y^2 \][/tex]
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