Question

plz do this sum for me

Answer 1

Answer:

Given:-

Simplify : ( 3x - 2y + z )² - 2 ( 3x - 2y + z ) ( x - 2y + z ) + ( x - 2y + z )²

To Find:-

The value of given sum.

Note:-

●》Here, we will first open bracket for calculations and if there is any number outside the bracket, it will be multiplied to it ( also if its power value, if power is outside the bracket, it will be multiplied to whole inside bracket value, also signs ) and then we will add or subtract the like terms according to their signs.

●》When same sign of two variables are multiplied, they becomes in square.

Solution:-

$\huge\red{( 3x - 2y + z )² - 2 ( 3x - 2y + z ) ( x - 2y + z ) + ( x - 2y + z )²}$

$\huge\red{\ \ \ \ Its \ \ value = ?}$

☆ According to note first point~

▪︎$( 3x - 2y + z )² - 2 ( 3x - 2y + z ) ( x - 2y + z ) + ( x - 2y + z )²$

▪︎$( 3x )² - ( 2y² ) + ( z² ) - ( 2 × 3x - 2 × 2y + 2 × z ) ( x - 2y + z ) + ( x² ) - ( 2y² ) + ( z² )$

▪︎$3x × 3x - 2y × 2y + z × z - ( 6x - 4y + 2z ) ( x - 2y + z ) + x × x - 2y × - 2y + z × z$

☆ According to note second point~

▪︎$9x² - 4y² + z² - 6x + 4y - 2z ↪ ( x - 2y + z ) + x² + 4y² + z²$

▪︎$9x² - 4y² + z² - 6x² - 12xy - 6xz + 4xy - 4y² + 4yz - 2xz + 4yz - 4z² + x² + 4y² + z²$

☆ Now, we will take like terms together for calculating~

▪︎$9x² - 6x² + x² - 4y² - 4y² + 4y² - 12xy + 4xy - 6xz - 2xz + 4yz + 4yz + z² - 4z² + z²$

☆ According to BODMAS, we will add first and where subtraction is needed, we will subtract and also common signs will be added~

▪︎$10x² - 6x² - 8y² + 4y² - 8xy - 8xz + 8yz - 4z² + 2z²$

☆ After adding or subtracting~

▪︎$4x² - 4y² - 8xy - 8xz + 8yz - 2z²$

$\huge\pink{Its \ \ value = 4x² - 4y² - 8xy - 8xz + 8yz - 2z²}$

Answer:-

Hence, the value of the given sum = 4x² - 4y² - 8xy - 8xz + 8yz - 2z² ( None of these ).