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

Which of the following is equal to (x + 2) (x + 9)?

• x² + 11x + 18

• x² + 18

• x² + 18x + 11

• x² + 3x + 11

Answer explanation

Since, (a+b)(a+c) = a² + (b + c)a + bc (x + 2) (x + 9) = x² +(2+9)x + 2 x 9 = x² + 11x + 18 Hence option 1 is correct.

Which of the following option is not equal to (100 + 5) (100 + 8)?

• 11340

• 105 x 108

• 100² + (5 + 8)(100) + 5 x 8

• 100² + 5² + 8²

Answer explanation

Since, (a + b)(a + c) = a² + (b + c)a + bc (100 + 5) (100 + 8) = 100² +( 5 + 8) x 100 + 5 x 8 = 10000 + 13 x 100 + 40 = 10000 + 1300 + 40 = 11340 Also, (100 + 5) (100 + 8) = 105 x 108 So, values of options 1, 2 and 3 are equal to (100 + 5) (100 + 8). Consider option 4, 100² + 5² + 8²= 10000 + 25 + 64 = 10089 ≠ 11340 Therefore, (100 + 5) (100 + 8) ≠ 100² + 5² + 8² Hence, option 4 is the correct answer.

(2xy + y)(2xy + x) is equal to ___________.

• 4x²y² + 2xy² + 2x²y

• 2x²y² + xy² + 2x²y

• 4x²y² + 2xy² + 2x²y + xy

• 2x²y² + xy² + 2x²y + xy

Answer explanation

Since (a + b)(a + c) = a² + (b + c)a + bc Therefore, (2xy + y)(2xy + x) = (2xy)² + (y + x) × (2xy) + xy = 2² × x² × y² + 2xy² + 2x²y + xy = 4x²y² + 2xy² + 2x²y + xy Therefore, option 3 is correct.

In a farm, there are (9x² + 23) cotton plants in each row. There are (9x² - 12) such rows. Which of the following correctly represents the total number of cotton plants in the farm?

• 81x⁴ + 99x² - 276

• 81x⁵ + 99x² - 99

• 9x⁷ + 99x - 276

• 9x⁴ + 99x² - 276

Answer explanation

Total number of plants = plants in each row × number of rows Total number of plants = (9x² + 23)(9x² - 12) = (9x² + 23)[9x² + (-12)] We know that (x + a) (x + b) = x² + (a + b)x + ab, So, we can write, (9x² + 23)[9x² + (-12)] = (9x²)² + [23 + (-12)] × (9x²) + 23 x (-12) = 9²(x²)² + 11 x (9x²) - 276 = 81x⁴ + 99x² - 276 Therefore, option 1 is correct.

If base of a parallelogram is (2x + 3) units and the height of parallelogram is (2x - 3) units, then what will be area of the parallelogram? (Take x = 8 units)

• 256 sq. units

• 64 sq. units

• 265 sq. units

• 247 sq. units

Answer explanation

Area of parallelogram = height of parallelogram × base of parallelogram = (2x + 3) (2x - 3) (2x + 3) (2x - 3) = (2x)² - 3² [by identity (a +b)(a - b) = a² - b²] = (2 × 8)² - 9 (taking x = 8 units) = (16)² - 9 = 256 - 9 = 247 sq. units So, option 4 is correct.