Find the product.

-a ^2 b ^2 c^ 2(a + b - c)

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gmany gmany · Answer 1 · 2018-09-25T22:53:44+02:00

[tex]\text{Use distributive property:}\\a(b + c) = ab + ac\\\\and\ a^n\cdot a^m=a^{n+m}[/tex]

[tex]-a^2b^2c^2(a+b-c)=(-a^2b^2c^2)(a)+(-a^2b^2c^2)(b)+(-a^2b^2c^2)(-c)\\\\=-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3[/tex]

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ColinJacobus ColinJacobus · Answer 2 · 2019-09-17T16:50:12+02:00

Answer: The required product is [tex]-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3.[/tex]

Step-by-step explanation: We are given to find the following product :

[tex]P=-a^2b^2c^2(a+b-c)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the given product, we must multiply the first common term to each term within the bracket.

The evaluation of the product (i) is as follows :

[tex]P\\\\=-a^2b^2c^2(a+b-c)\\\\=-a^2b^2c^2\times a-a^2b^2c^2\times b+a^2b^2c^2\times c\\\\=-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3.[/tex]

Thus, the required product is [tex]-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3.[/tex]