Question

(b) (x - y - z)(x2 + y2 + z2 + xy - yz + xz)​

Answer 1

Answer:

2bx² + 2bx²y -3bxyz + bx²z - 2by² - bxy² + by²z - 2bz² + byz² + bxz²

This problem was solved assuming that

x2 + y2 + z2 meant (x × 2) + (y × 2) + (z × 2) and not x² + y² + z²

Step-by-step explanation:

(b) (x - y - z)(x2 + y2 + z2 + xy - yz + xz)

This is a trinomial. Every term has to be multiplied with every other term.

The easiest way to do this is to do two of them first and the multiply their product with the third expression in brackets

(b) (x - y - z)(x2 + y2 + z2 + xy - yz + xz)

= [(b)(x - y - z)] ×(x2 + y2 + z2 + xy - yz +xz)

= (bx - by - bz) × (2x + 2y + 2z + xy - yz+ xz)

= bx(2x + 2y + 2z + xy - yz+ xz)-by(2x + 2y + 2z + xy - yz+ xz)-bz(2x + 2y + 2z + xy - yz+ xz)= (2bx² + 2bxy + 2bxz + 2bx²y - bxyz + bx²z)-(2bxy + 2by² + 2byz + bxy² - by²z + bxyz)-(2bxz + 2byz + 2bz² + bxyz - byz² + bxz²)

= 2bx² + 2bxy + 2bxz + 2bx²y - bxyz + bx²z

-2bxy - 2by² - 2byz - bxy² + by²z - bxyz

-2bxz - 2byz - 2bz² - bxyz + byz² - bxz²

= 2bx² + 2bxy - 2bxy + 2bxz - 2bxz + 2bx²y

-bxyz - bxyz - bxyz + bx²z - 2by² - 2byz

- 2byz - bxy² + by²z - 2bz² + byz² + bxz²

= 2bx² + 2bx²y -3bxyz + bx²z - 2by² - bxy² + by²z - 2bz² + byz² + bxz²