Question

Using (x+a) (x+b)= x²+(a+b) x+ab, find
9.7×9.8​

Answer 1

Given

• 9.7 × 9.8

Solution

• Using

$\large{\underline{\boxed{\tt{(x + a)(x + b) = x^2 + (a + b)x + ab}}}}$

⠀

★ We can right 9.7 × 9.8 as

$\tt:\implies{(10 - 0.3)(10 - 0.2)}$

⠀

$\sf\pink{⟶}$ Using the given identity, we can solve the further question.

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {(10)^2 + [(-0.3) + (-0.2)] × 9 + [(-0.3) × (-0.2)]}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {100 + [-0.5] × 10 + 0.06}$

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$\tt:\implies\: \: \: \: \: \: \: \: {(100 - 5) + 0.06}$

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$\tt:\implies\: \: \: \: \: \: \: \: {95 + 0.06}$

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$\tt:\implies\: \: \: \: \: \: \: \: {95.06}$

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Verification

$\tt:\implies{9.8 × 9.7 = 95.06}$

$\tt:\implies{95.06 = 95.06}$

$\tt:\implies{L.H.S = R.H.S}$

$\underline{\bf{\orange{Verified}}}$

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Answer 2

Firstly, we can also write 9.7×9.8 as,$\begin{lgathered}\\\end{lgathered}$

$\frak:\implies{(10 - 0.3)(10 - 0.2)}$

$\begin{lgathered}\\\end{lgathered}$

By using the identity,

${\underline{\overline{\red{\boxed{\blue{(x + a)(x + b) = x^2 + (a + b)x + ab}}}}}}$

$\begin{lgathered}\\\end{lgathered}$

Now,

$\begin{lgathered}:\implies\frak {(10)^2 + [(-0.3) + (-0.2)] × 9 + [(-0.3) × (-0.2)]}\\ \\\end{lgathered}$

$\begin{lgathered}\\\end{lgathered}$

$\begin{lgathered}:\implies\frak {100 + [-0.5] × 10 + 0.06}\\ \\\end{lgathered}$

$\begin{lgathered}\\\end{lgathered}$

$\begin{lgathered}:\implies\frak{(100 - 5) + 0.06}\\ \\\end{lgathered}$

$\begin{lgathered}\\\end{lgathered}$

$\begin{lgathered}:\implies\frak {95 + 0.06}\\ \\\end{lgathered}$

$\begin{lgathered}\\\end{lgathered}$

$\begin{lgathered}:\implies{\boxed{\frak{\purple{95.06}}}}\;\bigstar\\ \\\end{lgathered}$

$\begin{lgathered}\\\end{lgathered}$

━━━━━━━━━━━━━━━━━━━━━━

$\begin{lgathered}\\\end{lgathered}$

$\large{\pink{\underline{\tt{Let's\:explore\:more! ♡}}}}$

$\begin{lgathered}\\\end{lgathered}$

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$