Question

Add 3x(7x²-5x+3) and 2(x³-4x²+5)​​

Answer 1

Your answer is,

Step-by-step explanation:

multiplying the bracket,

$3x(7x^{2} -5x+3)$ + $2(x^{3}-4x^{2} +5)$

gives,

$(21x^{3} -15x^{2} +9x) + (2x^{3} -8x^{2} +5)$

solving this would give,

$23x^{3} -23x^{2} +9x+5$ will be our answer

Answer 2

★ Concept

In order to solve the above problem based on the concept of basic algebraic sum, first of all we have to multiply 3x and 2 with (7x²-5x+3) and (x³-4x²+5) respectively. The multiplication of these terms would be then followed by the summation(addition) of their products. The only thing to be noted is that while performing addition, only the terms having identical coefficient will be added to each other.

Let's proceed with calculation !!

⇒ 3x(7x²- 5x+3) + 2(x³- 4x²+5)

⇒ 21x³- 15x² + 9x + 2x³- 8x² + 10

⇒ (21 + 2)x³ - (15 + 8)x² + 9x + 10

⇒ 23x³ - 23x² + 9x + 10

Conclusion

23x³ - 23x² + 9x + 10 is thus, the resultant obtained.

$\underline{\rule{190pt}{2pt}}$

More to know

Note the above summation follows the algebraic rules of addition and the resultant obtained are written in decreasing order of the highest power of x .

☞ Algebraic Rules of Addition

While performing summation of algebraic terms :-

1. Two terms carrying positive sign will be added and the resultant so obtain will carry a positive sign.
2. Two terms carrying negative sign will also be added and the resultant so obtain will carry a negative sign.
3. Two terms carrying opposite signs will be subtracted and the resultant so obtain will carry the sign of the term greater among them.