Algebraic Identity I | Algebraic Expressions and Identities | Assessment | English | Grade 8

Choose the appropriate option to fill in the blank: (a + b)² = a² + ___ + b²

• 2a²b²

• ab

• 2ab

• a²b²

Answer explanation

Option 3 is the correct answer.

Which of the following options is not equal to 103²?

• 100² + 3²

• (100 + 3)(100 + 3)

• 100² + 3² + 2(3)(100)

• 10609

Answer explanation

We can write 103² as (100 + 3)² Since, (a + b)² = a² + 2ab + b² (100 + 3)² = 100² + 2 x 100 x 3 + 3² = 10000 + 600 + 9 = 10609 Here in option 1, 100² + 3² = 10000 + 9 = 10009 ≠ 10609 Therefore, option 1 is the correct answer.

The value of (x² + y²)² is __________.

• x² + 2x²y² + y²

• x² + 2xy + y²

• x⁴ + 4xy + y⁴

• x⁴ + 2x²y² + y⁴

Answer explanation

We know that, (a + b)² = a² + 2ab + b² here, a = x² so, a² = (x²)² = x⁴ and b = y² so, b² = (y²)² = y⁴ (x² + y²)² = x⁴ + 2x²y² + y⁴ Hence option 4 is correct.

Area of a square with side 5x + 9y is ___________.

• 25x² + 90xy + 81y²

• 5x² + 45xy + 9y²

• 25x² + 45xy + 81y²

• 5x² + 14xy + 9y²

Answer explanation

Area of square = side² = (5x + 9y)² Since, (a + b)² = a² +2ab + b² Therefore, (5x + 9y)² = (5x)² + 2 (5x) (9y) + (9y)² = 25x² + 90xy + 81y² Hence, option 1 is the correct answer.

The radius of a circle is given by 3x/2 + 4y/5. The area of the circle divided by π is ___________.

• 9x²/4π + 12xy/5π + 16y²/25π

• 9x²/4 + 12xy/5 + 16y²/25

• 3x²/2 + 2xy + 4y²/5

• x² + 12xy/5 + y²

Answer explanation

Let radius, r = 3x/2 + 4y/5 The area of the circle = πr² = π(3x/2 + 4y/5)² Since (a + b)² = a² + 2ab + b² Therefore, The area of the circle = π(3x/2 + 4y/5)² = π [(3x/2)² + 2 (3x/2) (4y/5) + (4y/5)²] = π [9x²/4 + 12xy/5 + 16y²/25] So, area of the circle divided by π = π[9x²/4 + 12xy/5 + 16y²/25]/π = 9x²/4 + 12xy/5 + 16y²/25 Therefore, option 2 is correct.

Simplify the expression given below: (3a + 2b)² - 3a² - 2b²

• 12ab

• 6a

• 6a² + 2b²

• 6a² + 12ab + 2b²

Answer explanation

We know that (x + y)² = x² + 2xy + y² So, (3a + 2b)² - 3a² - 2b² = (3a)² + 2 x 3a x 2b + (2b)² - 3a² - 2b² = 9a² + 12ab + 4b² - 3a² - 2b² = (9a² - 3a²) + 12ab + (4b² - 2b²) = 6a² + 12ab + 2b² Hence, option 4 is the correct answer.