Question

without actually calculating the cubes find the value of each of the following (-28)^3+(12)^3+(16)^3 ​

Answer 1

Answer:

-16128

Step-by-step explanation:

This expression can be calculated by algebraic means, whose process is described below:

1) $(-28)^{3}+(12)^{3}+(16)^{3}$ Given.

2) $(-12-16)^{3} + (12)^{3}+(16)^{3}$ Definition of addition.

3) $(-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}$ Cubic perfect binomial.

4) $(12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}$ Commutative property/$(-x)\cdot y = -x\cdot y$

5) $(12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)]$ Distributive property/$(-x)\cdot y = -x\cdot y$/$x^{n}\cdot y^{n} = (x\cdot y)^{n}$

6) $(12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)]$ $(-x)\cdot y = -x\cdot y$

7) $(-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)]$ Existence of the additive inverse/Modulative property for addition.

8) $(-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)]$ $x^{n}\cdot y^{n} = (x\cdot y)^{n}$/$(-x)\cdot (-y) = x\cdot y$

9) $(-3)\cdot (12)\cdot (16)\cdot (12+16)$ Distributive property.

10) $-16128$     $(-x)\cdot y = -x\cdot y$/Definition of sum/Definition of multiplication/Result