Question

# Subtract 4y(y - z + x) - 3x(x - y + z) from 5z(z - y - x)

Hint:

- The concept used in this question is the subtraction of polynomials.

○ Arrange the term in the decreasing order of their power.

○ To subtract polynomials simply subtract any like terms together.

○ Like terms are terms whose variables and exponents are the same

## The correct answer is: 3x2 – 4y2 + 5z2 – y z – 8xz – 7xy

### Answer:

Step by step explanation:

○ Given:

Terms:

4y (y - z + x) - 3x (x - y + z) ;

5z (z - y - x)

○ Step 1:

○ Subtract:

5z (z - y - x) - [4y (y - z + x) - 3x(x - y + z)]

(5z^{2} – 5yz – 5xz ) - [( 4y^{2} – 4yz + 4xy) - ( 3x^{2} -3xy – 3xz )

(5z^{2} – 5yz – 5xz ) - [4y^{2} – 4yz + 4xy - 3x^{2} + 3xy + 3xz )

(5z^{2} – 5yz – 5xz ) - 4y^{2} + 4yz - 4xy + 3x^{2} - 3xy - 3xz )

○ step 2:

○ Group the like terms.

(5z^{2}– 4y^{2} + 3x^{2}) + ( -5yz + 4yz) + (-5xz – 3xz) + (-4xy – 3xy)

(5z^{2}– 4y^{2} + 3x^{2}) + ( -yz ) + (-8xz) + (-7xy)

3x^{2} – 4y^{2} + 5z^{2} – yz – 8xz – 7xy

- Final Answer:

3x^{2} – 4y^{2} + 5z^{2} – yz – 8xz – 7xy

○ Step 1:

○ Subtract:

^{2}– 5yz – 5xz ) - [( 4y

^{2}– 4yz + 4xy) - ( 3x

^{2}-3xy – 3xz )

^{2}– 5yz – 5xz ) - [4y

^{2}– 4yz + 4xy - 3x

^{2}+ 3xy + 3xz )

^{2}– 5yz – 5xz ) - 4y

^{2}+ 4yz - 4xy + 3x

^{2}- 3xy - 3xz )

○ step 2:

○ Group the like terms.

^{2}– 4y

^{2}+ 3x

^{2}) + ( -5yz + 4yz) + (-5xz – 3xz) + (-4xy – 3xy)

^{2}– 4y

^{2}+ 3x

^{2}) + ( -yz ) + (-8xz) + (-7xy)

^{2}– 4y

^{2}+ 5z

^{2}– yz – 8xz – 7xy

^{2}– 4y

^{2}+ 5z

^{2}– yz – 8xz – 7xy