Algebraic Expressions and Identities | Chapter Assessment | English | Grade 8

If (3x⁴ + 3y⁴) is added to (5x⁴ + 2y⁴), then the number of terms in the result will be ______.

• Four

• Three

• Two

• One

Answer explanation

(3x⁴ + 3y⁴) + (5x⁴ + 2y⁴) = (3x⁴ + 5x⁴) + (3y⁴ + 2y⁴) = 8x⁴ + 5y⁴ So, there will be two terms in the result. Therefore, option 3 is correct.

Tags

CCSS.HSA.APR.A.1

Verify: (5p + 7q)² - 70pq = 25p² + 49q². Click on 'Yes' when it is done.

• Yes

• No

Answer explanation

Since, (a + b)² = a² + 2ab + b² (5p + 7y)² = (5p)² + 2 (5p) (7q) + (7q)² (5p + 7y)² = 25p² + 70 pq + 49q² (5p + 7y)² - 70 pq = 25p² + 49q² Hence verified.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.C.4

CCSS.HSA.APR.C.5

Evaluate (105)² and (48)² using appropriate identities. Click on 'Yes' when it is completed.

• Yes

• No

Answer explanation

We can write, (105)² = (100 + 5)² by using (a + b)² = a² + 2ab + b² (105)² = 100² + 2 (100) (5) + 5² (105)² = 10000 + 1000 + 25 = 11025 Similarly, we can write (48)² = (50 - 2)² by using (a - b)² = a² - 2ab + b² (48)² = 50² - 2 (50) (2) + 2² (48)² = 2500 - 200 + 4 = 2304

Tags

CCSS.6.EE.A.1

If P = (2a + 3) and Q = (4 - 3a), then what is the value of (P - Q)²?

• 4a² - 6a + 12

• 25a² - 10a + 12

• 25a² - 10a + 1

• 6a² - 6a + 12

Answer explanation

If P = (2a + 3) and Q = (4 - 3a) then, P - Q = (2a + 3) - (4 - 3a) = 2a + 3 - 4 + 3a = (5a -1) So, (P - Q)² = (5a -1)² Using (x - y)² = x² - 2xy + y² (P - Q)² = (5a)² - 2 (5a) (1) + (1)² = 5²a² - 10a + 1 = 25a² - 10a + 1 So, option 3 is correct.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

Simplify: (ab + bc + ac) (ab + bc + ac)

• 2 (ab + bc + ac)

• a²b² + b²c² + a²c² + 2ab²c + 2a²bc + 2abc²

• ab + bc + ac

• 2a²b² + 2b²c² + 2a²c² + 2ab²c + 2a²bc + 2abc²

Answer explanation

(ab + bc + ac) (ab + bc + ac) = ab (ab + bc + ac) + bc (ab + bc + ac) + ac (ab + bc + ac) = (ab x ab) + (ab x bc) + (ab x ac) + (bc x ab) + (bc x bc) + (bc x ac) + (ac x ab) + (ac x bc) + (ac x ac) = a²b² + ab²c + a²bc + ab²c + b²c² + abc² + a²bc + abc² + a²c² = a²b² + (ab²c + ab²c) + (a²bc + a²bc) + b²c² + (abc² + abc²) + a²c² = a²b² + 2ab²c + 2a²bc + b²c² + 2abc² + a²c² = a²b² + b²c² + a²c² + 2ab²c + 2a²bc + 2abc² Therefore, option 2 is correct.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.A.1

Value of (x + 3a)² - (3a - x)² is ________.

• 2x² - 12ax + 18a²

• 2x² + 12ax + 18a²

• 2x² + 18a²

• 12ax

Answer explanation

Since, (m + n)² = m² + 2mn + n² Also, (m - n)² = m² - 2mn + n² So, (x + 3a)² - (3a - x)² = x² + 2 × x × 3a + (3a)² - [(3a)² - 2 × (3a) × x + x²] = x² + 6ax + 9a² - [9a² - 6ax + x²] = x² + 6ax + 9a² - 9a² + 6ax - x² = (x² - x²) + (6ax + 6ax) + (9a² - 9a²) = 12ax Alternatively, Since, m² - n² = (m + n) (m - n) Therefore, (x + 3a)² - (3a - x)² = (x + 3a + 3a - x) [x + 3a - (3a - x)] = 6a (x + 3a - 3a + x) = 6a (2x) = 12ax So, option 4 is correct.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

What is the value of x² + 1/x², if x - 1/x = 4?

• 16

• 14

• 20

• 18

Answer explanation

Option 4 is the correct answer.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

What is the value of the below expression? (0.5x + 0.2y)² - (0.5x - 0.2y)²

• 0.25x² - 0.4y²

• 0

• 0.4xy

• x² - 0.04y²

Answer explanation

Let (0.5x + 0.2y)² = a and (0.5x - 0.2y)² = b Then, Since, a² - b² = (a + b) (a - b) Therefore, (0.5x + 0.2y)² - (0.5x - 0.2y)² = (0.5x + 0.2y + 0.5x - 0.2y) [0.5x + 0.2y - (0.5x - 0.2y)] = x (0.5x + 0.2y - 0.5x + 0.2y) = x (0.4y) = 0.4xy So, option 3 is correct.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2