Simplify the follow
following
(x² + 4y^2)² + (x²-4y²)^2
Answers
Answer: =2x4+32y4
Step-by-step explanation: Let's simplify your answer step-by-step.
(x2+4y2)2+(x2−4y2)2
Distribute:
=x4+8x2y2+16y4+x4+−8x2y2+16y4
Combine Like Terms:
=x4+8x2y2+16y4+x4+−8x2y2+16y4
=(x4+x4)+(8x2y2+−8x2y2)+(16y4+16y4)
=2x4+32y4
Solution!!
(x² + 4y²)² + (x² - 4y²)²
These kind of expressions can be solved using some algebraic identities and a few rules related to exponents. Therefore, it is advised to solve such questions if you know a few identities and the rules of the exponents.
Coming back to the question, we have to compare the first expression with the identity (a + b)² = a² + b² + 2ab.
= (x²)² + (4y²)² + 2(x²)(4y²) + (x² - 4y²)²
Simplify the expressions with a rule of exponents which is (aᵐ)ⁿ = aᵐⁿ.
= x⁴ + 4y⁴ + 8x²y² + (x² - 4y²)²
As the first expression is completely simplified, we'll simplify the second expression. Comparing it and expanding the second expression with the identity (a - b)² = a² + b² - 2ab.
= x⁴ + 16y⁴ + 8x²y² + (x²)² + (4y²)² - 2(x²)(4y²)
Simplify it further using the same rule of the exponents.
= x⁴ + 16y⁴ + 8x²y² + x⁴ + 16y⁴ - 8x²y²
As both the expressions are simplified, let's group the like terms.
= x⁴ + x⁴ + 16y⁴ + 16y⁴ + 8x²y² - 8x²y²
Calculate the sum and the difference.
= 2x⁴ + 32y⁴