Question

(4x^3 + 7y^3z^4)^2 .

A. (16x^6 + 56y^6z^8)
B. (8x^3 + 14y^3z^4)^2
C. (16x^3 + 49y^6z^8)
D. (16x^6 + 49y^6z^8)

Answer 1

The question incorrectly omits the cross-product terms from the binomial expansion of (4x^3 + 7y^3z^4)^2. The term without the cross-products is (16x^6 + 49y^6z^8), but this does not correctly apply the binomial theorem.

Step-by-step explanation:

The question asks to square the binomial (4x^3 + 7y^3z^4)^2. To do this, we apply the binomial theorem or use the FOIL method (First, Outer, Inner, Last). When we square the binomial, we must square each term and also consider the cross-product of the terms, multiplied by 2.

Squaring the first term: (4x^3)^2 = 16x^6.

Squaring the second term: (7y^3z^4)^2 = 49y^6z^8.

However, because the cross-product (2 × 4x^3 × 7y^3z^4) does not appear in the options, it means it must not have been a perfect square after all. So not taking into consideration the cross-products, which is incorrect in a standard binomial expansion, the closest option to the incorrect result would be: (16x^6 + 49y^6z^8).

Nonetheless, the correct full expansion of the square of the binomial should include the cross-products, which are not represented in any of the provided options.

Answer 2

The expression (4x^3 + 7y^3z^4)^2 becomes (16x^6 + 49y^6z^8) when each term inside the parentheses is squared and then added together.

Step-by-step explanation:

The expression (4x^3 + 7y^3z^4)^2 needs to be expanded by squaring both terms inside the parentheses. When you square a term, you multiply it by itself, so for the given expression, you would square 4x^3 to get 16x^6, and you would square 7y^3z^4 to get 49y^6z^8. Because these terms are being added together inside the parentheses and then squared, there are no cross terms in this case, so you simply add the squares of the individual terms to get the final result.

So, the expression squared will be (16x^6 + 49y^6z^8).