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

(x + 2) (x - 2) is equal to ________.

• x² - 2x + 4

• 4 - x² - 2x

• x² + 4

• x² - 4

Answer explanation

We know that, (a+b)(a-b) = a² - b² So, (x + 2) (x - 2) = x² - 4 Hence option 4 is correct.

Which of the following is not an identity?

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² + b² = (a + b) (a + b)

• a² - b² = (a + b) (a - b)

Answer explanation

Consider the equation given in option 3: a² + b² = (a + b) (a + b) Consider RHS = (a + b)(a + b) = a(a + b) + b(a + b) = a² + ab + ba + b² = a² + 2ab + b² ≠ LHS Therefore, equation in option 3 is not an identity whereas equations in options 1, 2 and 4 are all identities. Therefore, option 3 is the correct answer.

Which of the following is equal to (0.5x)² - (0.3y)²?

• (0.5x + 0.3y) (0.5x + 0.3y)

• (0.5x - 0.3y) (0.5x - 0.3y)

• (0.5x + 0.3y) (0.5x - 0.3y)

• None of the above

Answer explanation

As we know that a² - b² = (a + b) (a - b) So, (0.5x)² - (0.3y)² = (0.5x + 0.3y) (0.5x - 0.3y) Hence option 3 is correct answer.

Which of the following options is not equal to 68² - 32²?

• 3600

• (68 - 32)(68 + 32)

• (68 - 32)²

• 100 x 36

Answer explanation

We know that, (a+b)(a-b) = a² - b² We can write 68² - 32² = (68 + 32) (68 - 32) = 100 x 36 = 3600 Now consider (68 - 32)² = 68² + 32² - 2(68)(32) = 4624 + 1024 - 4352 = 1296 ≠ 3600 Therefore, (68 - 32)² ≠ 68² - 32² Therefore, option 2 is the correct answer.

Find the value of x, if 5500 x = (4800)² - (700)²

• 4100

• 5500

• 700

• 4800

Answer explanation

We know that, a² - b² = (a + b) (a - b) so, 5500 x = (4800)² - (700)² 5500 x = (4800 + 700) (4800 - 700) 5500 x = (5500) (4100) i.e., x = 4100 So, option 1 is correct.

Which of the following is equal to the following expression?

• 
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Answer explanation