Question

26.Using identities , Evaluate
(a)(2p-3a)2
(b)501x502
(c)(2x2+3x)2
(d) 194x206​

Answer 1

Answer:

a) (2p-3a)2

= 2p(2)-3a(2)

= 4p-6a or -6a+4p

b) 501×502

= (500+1)(500+2)

= 500(500+2)+1(500+2)

c) (2×2+3x)2

= (4+3x)2

= 4(2)+3x(2)

= 8+6x = 6x+8

d) 194×206

= (190+4)(200+6)

= 190(200+6)+4(200+6)

= 38006+806

= 38812

Answer 2

Solution :

(a) (2p - 3a)²

Using identity :

(a + b)² = a² + b² -2ab

➩ (2p)² + (3a)² - 2(2p)(3a)

➩ 4p² + 9a² - 12ap

━━━━━━━━━━━━━━━━━━━━━━

(b) 501 × 502

Using identity :

( x +a) (x + b) = x² + (a + b) x + ab

➫ (500)² + (1+2)500 + (1)(2)

➫ 250000 + 1500 + 2

➫ 251502

━━━━━━━━━━━━━━━━━━━━━━

(c) (2x² + 3x)²

Using identity :

( a +b) ² = a² + b² + 2ab

➪ (2x²)² + (3x)² + 2(2x²)(3x)

➪ 4x^4 + 9x² + 12x³

━━━━━━━━━━━━━━━━━━━━━━━

(d) 194 × 206

Using identity :

(x + a)(x + b) = x² + (a + b) x + ab

➭ ( 100 - 4) (100 +4)

➭ (100)² + ( - 4 + 4)100 + (-4)(4)

➭ 10000 + 100 - 16

➭ 10084