Algebraic Expressions and Equations

The video tutorial explains how to solve a quadratic equation by first squaring terms using the FOIL method, then distributing a negative sign, and combining like terms. The instructor demonstrates how to solve the equation by eliminating negatives and factoring to find the solutions, which are T = 10 and T = 2.

What is the result of expanding (T - 3)^2 using the FOIL method?

• T^2 - 6T + 9

• T^2 + 6T + 9

• T^2 + 9T - 6

• T^2 - 9T + 6

What is the next step after expanding (T - 3)^2 in solving the quadratic equation?

• Distribute a negative sign

• Add 11 to both sides

• Subtract 6T from both sides

• Multiply by 2

How do you handle a negative sign in front of a bracketed expression?

• Ignore it

• Add it to each term

• Distribute it to each term

• Multiply it by zero

What is the result of distributing the negative sign in the expression -1(T^2 - 6T + 9)?

• T^2 + 6T - 9

• T^2 - 6T + 9

• -T^2 + 6T - 9

• -T^2 - 6T + 9

What is the sum of the like terms 6T and 6T?

• 0

• 12T

• 6T

• 18T

After collecting like terms, what is the simplified form of the equation?

• -T^2 + 12T - 20 = 0

• T^2 - 12T + 20 = 0

• -T^2 + 12T + 20 = 0

• T^2 + 12T - 20 = 0

What operation is performed to eliminate the negative sign in front of the quadratic term?

• Add 1 to each term

• Multiply the equation by -1

• Divide the equation by 2

• Subtract 1 from each term

What is the factored form of the equation T^2 - 12T + 20 = 0?

• (T - 10)(T - 2)

• (T + 5)(T + 4)

• (T + 10)(T + 2)

• (T - 5)(T - 4)

What are the solutions to the equation T^2 - 12T + 20 = 0?

• T = 8 and T = 2

• T = 6 and T = 3

• T = 10 and T = 2

• T = 5 and T = 4

Which pair of numbers multiplies to 20 and adds to -12?

• 6 and 3

• 5 and 4

• 10 and 2

• 8 and 2