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In your own words, describe the process of multiplying binomials using the FOIL method. You can either write a paragraph describing the process, or you can list a set of steps to follow. Include an example problem in your answer.

Respuesta :

stevengeeky

Answer:

We can describe FOIL using the distributive property of multiplication. For real numbers x, y, and z the distributive property of multiplication states that

[tex](x + y)z = xz + yz[/tex]

Now let [tex]z = v + w[/tex], where v and w are real numbers.

Then [tex](x + y)(v + w) = x(v + w) + y(v + w)[/tex]

Here, we can again use the distributive property of multiplication to get

[tex]x(v + w) + y(v + w) = xv + xw + yv + yw[/tex]

Hence, it follows that

[tex](x + y)(v + w) = xv + xw + yv + yw[/tex]

This is the method of FOIL (first: xv, outside: xw, inside: yv, last: yw)

For example, [tex](1 + 2)(3 + 4) = 21 \\\text{and} \\1(3) + 1(4) + 2(3) + 2(4) = 3 + 4 + 6 + 8 = 21[/tex]

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