Question

Find the product of (4x10+9x7)(−4x10−9x7) .(1 point) Responses −16x20−72x17−81x14 negative 16 x to the 20th power minus 72 x to the 17th power minus 81 x to the 14th power −16x20−81x14 negative 16 x to the 20th power minus 81 x to the 14th power 16x20−72x17+81x14 16 x to the 20th power minus 72 x to the 17th power plus 81 x to the 14th power −16x100−72x70−81x49

Answer 1

To find the product of $(4x^{10}+9x^7)(-4x^{10}-9x^7)$, we can use the distributive property (also known as the FOIL method for binomials).

Let's denote:

• $A=4x^{10}$
• $B=9x^7$

Now, we rewrite the expression as: $$(A+B)(-A-B)$$

Now we can expand this:

$$=A(-A)+A(-B)+B(-A)+B(-B)$$ $$=-A^2-AB-AB-B^2$$ $$=-A^2-2AB-B^2$$

Calculating each term:

1. Calculate $A^2=(4x^{10}{)}^2=16x^{20}$.
2. Calculate $B^2=(9x^7{)}^2=81x^{14}$.
3. Calculate $AB=4x^{10}\cdot 9x^7=36x^{17}$.

Substituting these values into the expanded expression:

$$=-16x^{20}-2(36x^{17})-81x^{14}$$ $$=-16x^{20}-72x^{17}-81x^{14}$$

Thus, the product is: $$-16x^{20}-72x^{17}-81x^{14}$$

The correct response is: $-16x^{20}-72x^{17}-81x^{14}$