Multiply each of the following using a special product –
Example.1) (a+0.5)(a+0.4)
Ans.) (a+0.5)(a+0.4)
= a² + (0.5+0.4)a+ (0.4)(0.5)
[applying formula (x+a).(x+b)
= x² + (a+b)x + ab]
= a²+ 0.9a + 0.2 (Ans.)
Example.2) (a/5 +b/4)(a/4-b/7)
Ans.) (a/5 +b/4)(a/4-b/7)
a b a b
= ( --------- + --------- ) ( --------- - -------- )
5 4 4 7
[applying formula (x+a).(x-b) = x² + (a-b).x – ab]
a² 1 1 b²
= -------- + ( -------- - --------)ab - ---------
5.4 4.4 5.7 5.7
a² (35 – 16)ab b²
= --------- + --------------- - ----------
20 16.35 35
a² 19ab b²
= -------- + --------- - -------- (Ans.)
20 560 35
Example.3) ( 2xy – 0.4m)(2xy + 0.3m)
Ans.) (2xy – 0.4m)(2xy + 0.3m)
= (2xy)²- {(2X0.4) – (2X0.3)}mxy – (0.4X0.3)m²
[applying formula (x-a).(x+b) = x²- (a-b).x – ab]
= 4x²y²- (0.8 – 0.6)mxy – 0.12m²
= 4x²y²- 0.2mxy – 0.12m² (Ans.)
Example.4) (2ab-4xy)(0.2ab-2.1xy)
Ans.) (2ab-4xy)(0.2ab-2.1xy)
= (2X0.2)a²b²- {(4X0.2)+(4X2.1)}abxy + (4X2.1)x²y²
[applying formula (x-a).(x-b) = x²- (a+b)x + ab]
= 0.4a²b²- (0.8+8.4)abxy + 8.4x²y²
= 0.4a²b²- 9.2abxy + 8.4x²y² (Ans.)
mn 3mn
Example.5) (3l² - ---------)(4l² + ---------)
2 3
mn 3mn
Ans.) (3l² - ---------)(4l² + ----------)
2 3
4l²mn 3l².3mn 3m²n²
= (3l²X4l²) – {(---------) - (------------)} - -----------
2 3 3.2
[applying formula (x-a).(x+b) = x² - (a-b).x – ab]
m²n²
= 12l²⁺² - (2mnl²-3mnl²) - -----------
2
m²n²
= 12l⁴ - (-mnl²) - -----------
2
= 12l⁴ + mnl² - m²n²/2 (Ans.)