Question

Using (x + a) (x + b) = x2 + (a + b) x + ab, find​

Answer 1

Step-by-step explanation:

Formula used:

\begin{gathered}(x + a)(x + b) = {x}^{2} + (a + b)x + ab \\ \\ \end{gathered}

(x+a)(x+b)=x

2

+(a+b)x+ab

\begin{gathered}1) \: 103 \times 104 \\ \\ here \: x = 100 \: \: a = 3 \: \: \: b = 4 \\ \\ = > (100 + 3) \times (100 + 4) \\ \\ = > ( {100)}^{2} + (3 + 4) \times 100 + 3 \times 4 \\ \\ = > 10000 + 7 \times 100 + 12 \\ \\ = > 10000 + 700 + 12 \\ \\ = > 10712 \\ \\ \end{gathered}

1)103×104

herex=100a=3b=4

=>(100+3)×(100+4)

=>(100)

2

+(3+4)×100+3×4

=>10000+7×100+12

=>10000+700+12

=>10712

\begin{gathered}2) \: 5.1 \times 5.2 \\ \\ = > (5 + 0.1) \times (5 + 0.2) \\ \\ = > {(5)}^{2} + (0.1 + 0.2) \times 5 + 0.1 \times 0.2 \\ \\ = > 25 + 0.3 \times 5 + 0.02 \\ \\ = > 25 + 1.5 + 0.02 \\ \\ = > 26.52 \\ \\ \end{gathered}

2)5.1×5.2

=>(5+0.1)×(5+0.2)

=>(5)

2

+(0.1+0.2)×5+0.1×0.2

=>25+0.3×5+0.02

=>25+1.5+0.02

=>26.52

\begin{gathered}3) \: 103 \times 98 \\ \\ = > (100 + 3) \times (100 - 2) \\ \\ = > ( {100)}^{2} + (3 - 2) \times 100 - 2 \times 3 \\ \\ = > 10000 + 100 - 6 \\ \\ = > 10100 - 6 \\ \\ = > 10094 \\ \\ \end{gathered}

3)103×98

=>(100+3)×(100−2)

=>(100)

2

+(3−2)×100−2×3

=>10000+100−6

=>10100−6

=>10094

\begin{gathered}4) \: 9.7 \times 9.8 \\ \\ = > (10 - 0.3) \times( 10 - 0.2) \\ \\ = > ( {10)}^{2} - (0.2 + 0.3)10 + 0.3 \times 0.2 \\ \\ = > 100 - 5 + 0.06 \\ \\ = > 100.06 - 5 \\ \\ = > 95.06 \\ \\ \end{gathered}

4)9.7×9.8

=>(10−0.3)×(10−0.2)

=>(10)

2

−(0.2+0.3)10+0.3×0.2

=>100−5+0.06

=>100.06−5

=>95.06

Hope its help you

Answer 2

Step-by-step explanation:

105×107

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x 2

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x 2 +(a+b)x+ab]

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x 2 +(a+b)x+ab]⇒10000+1200+35

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x 2 +(a+b)x+ab]⇒10000+1200+35⇒11235

105×107⇒(100+5)(100+7) [is of the form (x+a)(x+b)]⇒(100 2 )+(7+5)(100)+7×5 [(x+a)(x+b)=x 2 +(a+b)x+ab]⇒10000+1200+35⇒11235∴105×107=11235.