Express (x + 6)2 as a trinomial in standard form.

Express (x + 6)2 as a trinomial in standard form.

The Correct Answer and Explanation is:

To express (x+6)2(x + 6)^2(x+6)2 as a trinomial in standard form, we need to expand it using the binomial expansion formula:(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2

Here, a=xa = xa=x and b=6b = 6b=6. Let’s apply the formula step by step:

1. Square the first term:

x2x^2×2

2. Multiply both terms and double the result:

2⋅x⋅6=12×2 \cdot x \cdot 6 = 12×2⋅x⋅6=12x

3. Square the second term:

62=366^2 = 3662=36

Now, combine all these terms:(x+6)2=x2+12x+36(x + 6)^2 = x^2 + 12x + 36(x+6)2=x2+12x+36

Thus, the trinomial in standard form is:x2+12x+36x^2 + 12x + 36×2+12x+36

Explanation:

1. Squaring the first term: In any binomial expression like (a+b)2(a + b)^2(a+b)2, squaring the first term gives you a2a^2a2, which in this case is x2x^2×2.
2. Doubling the product of the two terms: The term 2ab2ab2ab arises from multiplying both terms together and then doubling the product, which results in 12x12x12x.
3. Squaring the second term: Finally, squaring the second term, b=6b = 6b=6, gives us 363636.

So, when you expand (x+6)2(x + 6)^2(x+6)2, you end up with the trinomial x2+12x+36x^2 + 12x + 36×2+12x+36, which is in the standard form ax2+bx+cax^2 + bx + cax2+bx+c, where a=1a = 1a=1, b=12b = 12b=12, and c=36c = 36c=36.