Algebraic Expressions and Equations

The video tutorial covers three algebra problems involving perfect square trinomials and solving equations. Problem 23 focuses on identifying and solving a perfect square trinomial. Problem 24 involves finding the possible values of R + S using the properties of perfect squares. Problem 25 requires calculating the value of 5R + 10S by manipulating given equations and recognizing patterns in algebraic expressions.

What is the first step in solving the equation 2x + 3y = 4 to find the value of 4x² + 12xy + 9y²?

• Multiply both sides by 2

• Take the square of both sides

• Subtract 2x from both sides

• Add 3y to both sides

How do you confirm that 4x² + 12xy + 9y² is a perfect square trinomial?

• Check if 4x² and 9y² are perfect squares

• Multiply 2x by 3y and double it

• Add 4x² and 9y²

• Subtract 12xy from 4x²

What is the value of 4x² + 12xy + 9y² when 2x + 3y = 4?

• 24

• 20

• 16

• 12

What is the expression R² + 2RS + S² equivalent to?

• (R + S)²

• R + S

• R - S

• R + S²

If R² + 2RS + S² = 81, what are the possible values of R + S?

• 9 and -9

• 8 and -8

• 7 and -7

• 6 and -6

What is the correct answer choice for R + S if positive 9 is not an option?

• Negative 8

• Positive 8

• Negative 9

• Positive 9

What is the value of a + b if a² + b² = r and a + b = 8?

• 8

• 9

• 6

• 7

How do you express 5r + 10s in terms of a and b?

• 5(a + b)² - 10ab

• 5(a + b)² + 10ab

• 5(a² + b²) + 10ab

• 5(a² - b²) + 10ab

What is the value of 5r + 10s if a + b = 8?

• 320

• 300

• 260

• 280

What is the result of 5 times 8 squared?

• 360

• 280

• 320

• 400