Expansions — Exercise 3(C)

Write down the following products:

(x + 6)(x + 2)

Answer

(i) Given,

⇒ (x + 6)(x + 2)

⇒ (x² + 2x + 6x + 12)

⇒ (x² + 8x + 12).

Hence, (x + 6)(x + 2) = (x² + 8x + 12).

Write down the following products:

(x + 8)(x - 3)

Answer

Given,

⇒ (x + 8)(x - 3)

⇒ (x² - 3x + 8x - 24)

⇒ (x² + 5x - 24).

Hence, (x + 8)(x - 3) = (x² + 5x - 24).

Write down the following products:

(x - 5)(x - 7)

Answer

Given,

⇒ (x - 5)(x - 7)

⇒ (x² - 7x - 5x + 35)

⇒ (x² - 12x + 35).

Hence, (x - 5)(x - 7) = (x² - 12x + 35).

Write down the following products:

(2 - x)(4 - x)

Answer

Given,

⇒ (2 - x)(4 - x)

⇒ (8 - 2x - 4x + x²)

⇒ (8 - 6x + x²).

Hence, (2 - x)(4 - x) = (8 - 6x + x²).

Write down the following products:

(y - 7)(y + 4)

Answer

Given,

⇒ (y - 7)(y + 4)

⇒ (y² + 4y - 7y - 28)

⇒ (y² - 3y - 28).

Hence, (y - 7)(y + 4) = (y² - 3y - 28).

Write down the following products:

(ab + 3)(ab - 2)

Answer

Given,

⇒ (ab + 3)(ab - 2)

⇒ (a²b² - 2ab + 3ab - 6)

⇒ (a²b² + ab - 6).

Hence, (ab + 3)(ab - 2) = (a²b² + ab - 6).

Write down the following products:

(5 - xy)(2 + xy)

Answer

Given,

⇒ (5 - xy)(2 + xy)

⇒ (10 + 5xy - 2xy - x²y²)

⇒ (10 + 3xy - x²y²).

Hence, (5 - xy)(2 + xy) = (10 + 3xy - x²y²).

Write down the following products:

(x² + 1)(x² + 2)

Answer

Given,

⇒ (x² + 1)(x² + 2)

⇒ (x⁴ + 2x² + x² + 2)

⇒ (x⁴ + 3x² + 2).

Hence, (x² + 1)(x² + 2) = (x⁴ + 3x² + 2).

Write down the following products:

(3 - x²)(5 + x²)

Answer

Given,

⇒ (3 - x²)(5 + x²)

⇒ (15 + 3x² - 5x² - x⁴)

⇒ (15 - 2x² - x⁴).

Hence, (3 - x²)(5 + x²) = (15 - 2x² - x⁴).

Write down the following products:

(6 - x)(x + 5)

Answer

Given,

⇒ (6 - x)(x + 5)

⇒ (6x + 30 - x² - 5x)

⇒ (30 - x² + x).

Hence, (6 - x)(x + 5) = (30 - x² + x).

Write down the following products:

(2x + 3)(3x + 5)

Answer

Given,

⇒ (2x + 3)(3x + 5)

⇒ (6x² + 10x + 9x + 15)

⇒ (6x² + 19x + 15).

Hence, (2x + 3)(3x + 5) = (6x² + 19x + 15).

Write down the following products:

(7m - 2)(4m + 3)

Answer

Given,

⇒ (7m - 2)(4m + 3)

⇒ (28m² + 21m - 8m - 6)

⇒ (28m² + 13m - 6).

Hence, (7m - 2)(4m + 3) = (28m² + 13m - 6).

Write down the following products:

(2y - 3)(3y - 5)

Answer

Given,

⇒ (2y - 3)(3y - 5)

⇒ (6y² - 10y - 9y + 15)

⇒ (6y² - 19y + 15).

Hence, (2y - 3)(3y - 5) = (6y² - 19y + 15).

Write down the following products:

(3a² - b²)(2a² + 5b²)

Answer

Given,

⇒ (3a² - b²)(2a² + 5b²)

⇒ (6a⁴ + 15a²b² - 2a²b² - 5b⁴)

⇒ (6a⁴ + 13a²b² - 5b⁴).

Hence, (3a² - b²)(2a² + 5b²) = 6a⁴ + 13a²b² - 5b⁴.