Question

Statement A: (a + b)² = (a-b)² + 4ab.
Statement B: (a+b)² + (a-b)² = 4ab 
true or false?​

Answer 1

Hiiii

Answer:

statement a- True

statement b- false

Step-by-step explanation:

*STATEMENT A*

(a+b)²=(a-b)² +4ab

let's solve

using identities

(a + b)²=a² + b² + 2ab and (a - b)²= a² + b² - 2ab

Therefore,

a² + b² + 2ab = a² + b² - 2ab + 4ab

a² + b² + 2ab = a² + b² + 2ab

it means its true

*STATEMENT B*

(a+b)² + (a-b)² = 4ab 

using identities

(a + b)²=a² + b² + 2ab and (a - b)²= a² + b² - 2ab

Therefore,

a² + b² + 2ab + a² + b² - 2ab = 4ab

a² + a²+ b² + b² + 2ab - 2ab = 4ab

2a² + 2b² + 0 =4ab

so 2a² + 2b² is not equals to 4ab

it means its false

please mark as brainliest❤

Have a good day

Answer 2

A N S W E R :

1. Statement A – True
2. Statement B – False

1). Given :

• Statement A

• ${\sf{\bigg(a\;+\;b\bigg)^2\:=\; \bigg(a\:-\:b\bigg)^2\:+\:4ab}}$

To find :

• Find True or False ?

$\large\star$ As we know that,

$\large\dag$ Used identify

• $\boxed{\bf{\bigg(a\:+\:b\bigg)^2\:=\:a^2\:+\:b^2\:+\;2ab}}$

Solution :

• ${\sf{a^2\:+\;b^2\:+\:2ab\:=\:a^2\:+\;b^2\:-\:2ab\:+\:4ab}}$

• ${\sf{a^2\:+\;b^2\:+\:2ab\:=\:a^2\:+\;b^2\:+\:2ab}}$

Hence,

• ${\underline{\textsf{It\;means\; \textbf{Statement\:A}\:its\; \textbf{True}.}}}$

$~~~~~~~~~~~~~$ ________________________

2). Given :

• Statement B

• ${\sf{\bigg(a\;+\;b\bigg)^2\:+\; \bigg(a\:-\:b\bigg)^2\:=\:4ab}}$

To find :

• Find True or False ?

$\large\star$ As we know that,

$\large\dag$ Used identify

• $\boxed{\bf{\bigg(a\:-\:b\bigg)^2\:=\:a^2\:+\:b^2\:-\;2ab}}$

Solution :

• ${\sf{a^2\:+\:b^2\:+\:2ab\:a^2\:+\:b^2\:-\:2ab\:=\:4ab}}$

• ${\sf{a^2\:+\:a^2\:+b^2\:+\;b^2\:+\:2ab\:-\:2ab\:=\:4ab}}$

• ${\sf{2a^2\:+\:2b^2\:+\:0\:=\:4ab}}$

• ${\sf{2ab^2\:+\:2ab^2\:is\:not\:equals\:to\:4ab}}$

Hence,

• ${\underline{\textsf{It\;means\; \textbf{Statement\:B}\:its\; \textbf{False}.}}}$

$~~~~$$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

$~~~~~~~~~~~~~$ ________________________