How do you find the product #(5x^2-y^2)^2#?

Answer 1

See the entire solution process below:

First, we can rewrite this expression as:

#(5x^2 - y^2)(5x^2 - y^2)#

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(5x^2) - color(red)(y^2))(color(blue)(5x^2) - color(blue)(y^2))# becomes:
#(color(red)(5x^2) xx color(blue)(5x^2)) - (color(red)(5x^2) xx color(blue)(y^2)) - (color(red)(y^2) xx color(blue)(5x^2)) + (color(red)(y^2) xx color(blue)(y^2))#
#25x^4 - 5x^2y^2 - 5x^2y^2 + y^4#

We can now combine like terms:

#25x^4 + (-5 - 5)x^2y^2 + y^4#
#25x^4 -10x^2y^2 + y^4#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the product of (5x^2 - y^2)^2, you can use the formula for squaring a binomial, which is (a - b)^2 = a^2 - 2ab + b^2. Applying this formula to (5x^2 - y^2)^2, you would square each term individually and combine them using the formula. So, the result would be:

(5x^2 - y^2)^2 = (5x^2)^2 - 2(5x^2)(y^2) + (y^2)^2 = 25x^4 - 10x^2y^2 + y^4.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7