QuestionSimplify $(1+4 x)(3 x^{2}-2 x)+(x-3)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(1+4 x)\left(3 x^{}- x\right)+(x-3)$ . We need to simplify this expression

STEP 2

First, we need to distribute the terms in the first parentheses to the terms in the second parentheses. This is done by multiplying each term in the first parentheses by each term in the second parentheses.
$(1+4 x)\left( x^{2}-2 x\right) =1 \cdot ( x^{2}-2 x) +4x \cdot ( x^{2}-2 x)$

STEP 3

Now, distribute the terms.
$1 \cdot (3 x^{2}-2 x) =3 x^{2} -2x$ $x \cdot (3 x^{2}-2 x) =12 x^{3} -8x^{2}$

STEP 4

Combine these two results.
$3 x^{2} -2x +12 x^{3} -8x^{2} =12 x^{3} + (3 x^{2} -8x^{2}) -2x$

STEP 5

implify the expression by combining like terms.
$12 x^{3} + (3 x^{2} -8x^{2}) -2x =12 x^{3} -5x^{2} -2x$

STEP 6

Now, add the last term $(x-3)$ to the simplified expression.
$12 x^{3} -5x^{2} -2x + (x-3) =12 x^{3} -5x^{2} -2x + x -3$

STEP 7

Finally, simplify the expression by combining like terms.
$12 x^{3} -5x^{2} -2x + x -3 =12 x^{3} -5x^{2} - x -3$ So the simplified form of the given expression is $12 x^{3} -5x^{2} - x -3$ .

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