Expand the expression to a polynomial in standard form: $$ \left(3 x^{2}+x-4\right)\left(x^{2}-x+4\right) $$

Question

UpStudy AI · Accepted Answer

Calculate the expanded algebra expression $$ (3x^2+x-4)(x^2-x+4) $$.
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(3x^{2}+x-4ight)\left(x^{2}-x+4ight)$$
- step1: Apply the distributive property:
  $$3x^{2}	imes x^{2}-3x^{2}	imes x+3x^{2}	imes 4+x	imes x^{2}-x	imes x+x	imes 4-4x^{2}-\left(-4xight)-4	imes 4$$
- step2: Multiply the terms:
  $$3x^{4}-3x^{3}+12x^{2}+x^{3}-x^{2}+4x-4x^{2}-\left(-4xight)-16$$
- step3: Remove the parentheses:
  $$3x^{4}-3x^{3}+12x^{2}+x^{3}-x^{2}+4x-4x^{2}+4x-16$$
- step4: Add the terms:
  $$3x^{4}-2x^{3}+7x^{2}+8x-16$$
The expanded expression in standard form is $$3x^{4}-2x^{3}+7x^{2}+8x-16$$.
The expanded expression is $$3x^{4}-2x^{3}+7x^{2}+8x-16$$.

Expand the expression to a polynomial in standard form:

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions