Carry The Two

Radical A radical is the term under a square root symbol.   In the picture above, x would be the radical. Cube Root The expression for cube root is a small 3 above the radical/to the left.   This number is called the index.   To calculate the cube root of a number, we must find the number multiplied by itself, and then multiplied by itself again, is equaled to the original number. Problem #1 What is the cube root of 8? Step 1 We ask ourselves: What number multiplied by itself twice, equals 8? Step 2 Guess and check: Try 2 2 x 2 x 2 = 8 Therefore the cube root of 8 = 2 Answer: 2 Further Explanation Taking the cube root of a number is the inverse of cubing, therefore the answer is 2 because 2 3 = 8. If Problem #1’s explanation does not make sense, lets think about what we do when we cube a number. To cube a number, we multiply it 3 times. For example, when we cube the number 5: 5 x 5 x 5 = 125 A cube root goes in the...

PROBLEM #1 (4x - 4)(x + 4) FOIL First Outside Inside Last Step One First: • The first term in the first binomial is 4x • The first term in the second binomial is x • So we multiply them: (4x)(x) = 4x2 Step Two Outside: • The outside term in the first binomial is 4x • The outside term in the second binomial is 4 • So we multiply them: (4x)(4) = 16x Step Three Inside: • The inside term in the first binomial is - 4 • The inside term in the second binomial is x • So we multiply them: (- 4)(x) = - 4x Step Four Last: • The last term in the first binomial is - 4 • The last term in the second binomial is 4 • So we multiply them: (- 4)(4) = - 16 Step Five • Write out your calculations as one equation: • 4x2 + 16x – 4x – 16 Step Six • Combine like terms • The 16x and - 4x are the only set of terms that are like • 16x – 4x = 12x • Therefore your answer is: ANSWER 4x2 + 12x – 16 PROBLEM #2 (4x - 4)(3x + 2) FOIL First Outside ...

PROBLEM #1 Solve for x. -24 - 3x = 9x Step One Add 3x to each side: (You are attempting to get your variables (x's) on one side) -24 = 12x Step Two Divide both sides by 12 (You divide by 12 in order to get the x by itself) -2 = x Step Three Check your answer by plugging in the -2 for the x's in the original equation: -24 - 3(-2) = 9(-2) -24 + 6 = -18 -18 = -18 -18 does equal -18 therefore we know our answer (x = -2) is correct. PROBLEM #2 Solve for x. 4x = -8 + 5x Step One Subtract 5x from each side: (You are attempting to get your variables (x's) on one side) -x = -8 Step Two Use logical reasoning to determining what x is equaled to, considering you know what negative x equals: If -x = -8, then x = 8 Step Three Check your answer by plugging in the 8 for the x's in the original equation: 4(8) = -8 + 5(8) 32 = -8 + 40 32 = 32 32 does equal 32 therefore we know our answer (x = 8) is correct.