Question

Why is the middle term 2ab in (a + b)2 and −2ab in (a − b)2 when written in standard form?

Answer 1

Answer:

because 2ab has addition symbol and-2ab has minus symbol so 2(a+b)or (a+b)2 and-2ab in (a-b)2 is possible

Answer 2

By using distributive principle we prove that, the middle term 2ab in$(a + b)^2$ and −2ab in $(a -b)^2$ when written in standard form.

When we use the distributive principle to extend the equation $(a+b)^2$, we get:

$(a + b)^2 = (a + b)(a + b) = a(a + b) + b(a + b)$

When we summarize this equation, we obtain:

$(a + b)^2 = a^2 + ab + ab + b^2$

Terms a and b can also be combined to create:

$(a + b)^2 = a^2 + 2ab + b^2$

So, the middle term in $(a + b)^2$ is 2ab.

After expanding the expression $(a - b)^2$ using the distributive property, we get:

$(a - b)^2 = (a - b)(a - b) = a(a - b) - b(a - b)$

By simplify this expression, we get:

$(a - b)^2 = a^2 - ab - ab + b^2$

Yet again, the terms -ab and -ab are two that refer to the result of a and b. These terms can be combined to create:

$(a - b)^2 = a^2 - 2ab + b^2$

Hence, the middle term in $(a - b)^2$ is -2ab.

Hence, the middle term 2ab in $(a + b)^2$ and -2ab in $(a - b)^2$ when written in standard form.

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