Question

Use the formula:(a+b)(a-b)=a square-b square to evaluate
1. 105*95
2.4.6*5.4​

Answer 1

Answer:

105×95

= (100+5)(100-5)

=100²-5²

=10000-25

=9975

4.6×5.4

=(5-0.4)×(5+0.4)

=5²-0.4²

=25-0.16

=24.84

Answer 2

$\huge{\underline{\boxed{\boxed{\red{\mathcal{QUESTION:}}}}}}$

Use the formula: (a + b)(a - b) = a² - b² to evaluate :

1. 105 × 95
2. 5.4 × 4.6

$\huge{\underline{\boxed{\boxed{\red{\mathcal{SOLUTION:}}}}}}$

$\star{\underline{\blue{\bf{Formula\;Used:}}}}$

• (a + b)(a - b) = a² - b²

1). 105 × 95

⇒ (100 + 5)(100 - 5)

⇒ (a + b)(a - b) = a² - b²

⇒ 100² - 5²

⇒ 10000 - 25

⇒ 9,975

2). 5.4 × 4.6

⇒ (5 + 0.4)(5 - 0.4)

⇒ (a + b)(a - b) = a² - b²

⇒ 5² - 0.4²

⇒ 25 - 0.16

⇒ 24.84

$\star{\underline{\blue{\bf{Extra\;Info:}}}}$

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