Question

Multiply:
(i) x² +y² +z² -xy+xz+yzbyx+y-z
(ii) x² +4y² +z² +2xy+xz-2yzbyx-2y-z
(iii) x² +4y² +2xy+-3x+6y+9byx-2y+3
(iv) 9x² +25y² +15xy+12x-20y+16by3x-5y+4

Answer 1

Answer:

1. $x^3+y^3-z^3+3xyz$
2. $x^3-8y^3-z^3-6xyz$
3. $x^3-8y^3-18xy+27$
4. $27x^3-125y^3+180xy+64$

Step-by-step explanation:

First, find the suitable identity.

Here we have $(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc$.

(i) Here, $a=x$, $b=y$, and $c=-z$.

Answer is $x^3+y^3-z^3+3xyz$.

(ii) Here, $a=x$, $b=-2y$, and $c=-z$.

Answer is $x^3-8y^3-z^3-6xyz$.

(iii) Here, $a=x$, $b=-2y$, and $c=3$.

Answer is $x^3-8y^3-18xy+27$.

(iv) Here, $a=3x$, $b=-5y$, $c=4$.

But we have $(3x-5y+4)(9x^2+25y^2+15xy+12x-20y+16)$.

If you look carefully, you can find that identity couldn't be used.

Because it's $(a+b+c)(a^2+b^2+c^2+ab+bc+ca)$.

I think you made typing error. I will continue.

Answer is $27x^3-125y^3+180xy+64$.

Answer 2

First, find the suitable identity.

Here we have (a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)=a

3

+b

3

+c

3

−3abc .

(i) Here, a=xa=x , b=yb=y , and c=-zc=−z .

Answer is x^3+y^3-z^3+3xyzx

3

+y

3

−z

3

+3xyz .

(ii) Here, a=xa=x , b=-2yb=−2y , and c=-zc=−z .

Answer is x^3-8y^3-z^3-6xyzx

3

−8y

3

−z

3

−6xyz .

(iii) Here, a=xa=x , b=-2yb=−2y , and c=3c=3 .

Answer is x^3-8y^3-18xy+27x

3

−8y

3

−18xy+27 .

(iv) Here, a=3xa=3x , b=-5yb=−5y , c=4c=4 .

But we have (3x-5y+4)(9x^2+25y^2+15xy+12x-20y+16)(3x−5y+4)(9x

2

+25y

2

+15xy+12x−20y+16) .

If you look carefully, you can find that identity couldn't be used.

Because it's (a+b+c)(a^2+b^2+c^2+ab+bc+ca)(a+b+c)(a

2

+b

2

+c

2

+ab+bc+ca) .

I think you made typing error. I will continue.

Answer is 27x^3-125y^3+180xy+6427x

3

−125y

3

+180xy+64 .