Algebraic Expression and Identities

 Find the product of the following pairs of monomials.

(i) 4, 7p

• 4 , 7 p =  4 7 × p = 28p

• 4p ×  0 = 0

• – 4p × 7pq =(-4 × 7 ) (p × pq) =  -28p²q

• 4p³ × – 3p = (4 × -3 ) (p³ × p ) =  -12p⁴

 Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) 5a, 3a², 7a⁴

• x² + 10x + 21

• 4a⁴ + 28a² + 45

• 5a x 3a² x 7a⁴ = (5 × 3 × 7) (a × a² × a⁴ ) = 105a⁷

• x2y2z2 – 6xyz + 8

Find the following squares by using the identities.

[(2m/3) + (3n/2)]²

• (b – 7)² = b² – 14b + 49

• (12.1 + 7.9)(12.1 – 7.9) = 20 x 4.2= 84

• 81p² + 90pq + 25q²

• [(2m/3}) + (3n/2)]² = (4m²/9) +(9n²/4) + 2mn

 Show that

(3x + 7)² – 84x = (3x – 7)²

• 81p² + 90pq + 25q²

• 9x² – 42x + 49 = RHS

  LHS = RHS

• none of the

  above

Which of the following numbers is a perfect cube ?

(a) 125

(b) 36

(d) 75

(E) 100

• (d) 75

• (b) 36

• (a) 125

• (d) 100

• 𝑥2+6𝑥+9

The cube of an odd natural number is

(a) even

(b) odd

(c) may be even, may be odd

(d) prime number

• prime number

• may be even, may be odd

• odd

• EVEN

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products.

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

• 4x² + 16xy + 15y²

• 16x² – 24x + 5

• x²y²z² – 6xyz + 8

• 4a⁴ + 28a² + 45

If it takes 40 days for 120 men to complete a work, how long will it take for 80 men to complete the same work?

8 g of sandal wood cost Rs 40. What will 10 g cost ?

(a) Rs 30

(b) Rs 36

(c) Rs 48

(d) Rs 50

• RS 50

• RS 48

• RS 36

• RS 30