Question

using the formula ₍a + b₎² for squaring a binomial, evaluate it:₍54₎²

Answer 1

Answer:

2916

Step-by-step explanation:

(a+b)² = (a² +2ab +b²)

54 = 50 + 4

here a = 50 and b = 4

using the formula,

=> ( 50² + 2(50)(4) + 4² )

=> (2500 + 400 + 16)

=> (2916)

Answer 2

Given:

• (54)²

Find:

• Solve by using (a+b)²

Solution:

$\textsf{we, have}$

$\sf:\to {(54)}^{2}$

$\sf{which\:we\:can\:write\:as\:(50+4)^2}$

$\sf:\to {(54)}^{2}$

$\sf:\to {(50 + 4)}^{2}$

$\sf{Using\:(a+b)^2 = a^2 + b^2 + 2ab}$

$\sf:\to {(50 + 4)}^{2}$

$\sf:\to {(50)}^{2} + {(4)}^{2} + 2(50)(4)$

$\sf:\to 2500+16+ 2(200)$

$\sf:\to 2500+16+ 400$

$\sf:\to 2500+ 416$

$\sf:\to 2916$

Hence, (54)² = 2916

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$\huge{\textbf{More Info.}}$

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