Question

8. Using (x + a) (x + b) = x2 + (a + b) x + ab, find (1) 103 x 104 (ii) 5.1 x 5.2 (iii) 103 x 98 iv 9.7*9.8​

Answer 1

$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$

Step-by-step explanation:

$\begin{aligned} \rm(i) \quad 103 \times 104 &=(100+3) \times(100+4)\\ \\ &=(100)^{2}+(3+4) \times 100+3 \times 4 \\ &=10000+700+12 \\ &\red{=10712 }\\\\(\text { ii }) \quad 5.1 \times 5.2 \\ \\ &=(5+0.1)(5+0.2)\\ &=(5)^{2}+(0.1+0.2) \times 5+0.1 \times 0.2\\&=25+1.5+0.02 \\ &\blue{=26.52} \\\\(\text { iii }) \quad 103 \times 98 \\ &=(100+3)(100-2)=(100+3)[100+(-2)] \\ \\ &=(100)^{2}+[3+(-2)] \times 100+3 \times(-2) \\ \\ &=10000+(3-2) \times 100-6\\ \\ &=10000+100-6 \\ \\ &\green{=10094 }\\\\(\text { iv }) \quad 9.7 \times 9.8 \\ \\ &=(9+0.7)(9+0.8)\\ \\ &=(9)^{2}+(0.7+0.8) \times 9+0.7 \times 0.8\\ \\ &=81+13.5+0.56 \\ \\ &\orange{=95.06 }\end{aligned}$

Answer 2

Answer:

Answer is attached here.