Question

(2у-3)(3у+1)+2(у-5)(у+5)=2(1-2у)²+6у

Answer 1

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Answer 2

Let's simplify both sides of the equation step by step to see if they are equal:

Left-hand side (LHS): (2у - 3)(3у + 1) + 2(у - 5)(у + 5)

Using the distributive property: LHS = 2у * 3у + 2у * 1 - 3 * 3у - 3 * 1 + 2(у * у + у * 5 - 5 * у - 5 * 5)

Simplify: LHS = 6у² + 2у - 9у - 3 + 2(у² + 5у - 5у - 25)

Combine like terms: LHS = 6у² + 2у - 9у - 3 + 2(у² - 25)

Simplify the expression inside the parentheses: LHS = 6у² + 2у - 9у - 3 + 2у² - 50

Combine like terms again: LHS = 6у² + 2у² - 9у + 2у - 53

Combine the terms with the same variable: LHS = 8у² - 7у - 53

Right-hand side (RHS): 2(1 - 2у)² + 6у

Since (1 - 2у)² is the same as (1 - 2у)(1 - 2у), we can use the distributive property again:

RHS = 2(1 - 2у)(1 - 2у) + 6у

Using the distributive property again: RHS = 2(1 * 1 - 1 * 2у - 2у * 1 + 2у * 2у) + 6у

Simplify: RHS = 2(1 - 4у + 4у²) + 6у

Using the distributive property one more time: RHS = 2 - 8у + 8у² + 6у

Combine like terms: RHS = 8у² - 2у + 2

Now the equation becomes: 8у² - 7у - 53 = 8у² - 2у + 2

Subtracting the common terms on both sides: -7у - 53 = -2у + 2

Adding 7у to both sides: -53 = 5у + 2

Subtracting 2 from both sides: -55 = 5у

Dividing both sides by 5: у = -11

After simplification, the value of у that satisfies the equation is -11.