QuestionMultiply and simplify: $3 x^{2}(9 x^{5}-4 x^{2}+5)$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3 x^{}\left(9 x^{5}-4 x^{}+5\right)$ . We are asked to multiply and simplify this expression if necessary.

STEP 2

We can simplify this expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c a(b + c) = ab + a*c.
In this case, we distribute $x^{2}$ to each term inside the parentheses.

STEP 3

Multiply $3 x^{2}$ with each term inside the parentheses.
$3 x^{2} 9 x^{5} -3 x^{2} x^{2} +3 x^{2} *5$

STEP 4

implify each term.
The multiplication of two exponents with the same base (in this case, x) can be simplified by adding the exponents.So, $x^{2} * x^{} = x^{2+} = x^{7}$

STEP 5

Apply the simplification to each term.
$27 x^{7} -12 x^{4} +15 x^{2}$ This is the simplified form of the given expression.

Was this helpful?

QuestionMultiply and simplify: $3 x^{2}(9 x^{5}-4 x^{2}+5)$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3 x^{}\left(9 x^{5}-4 x^{}+5\right)$ . We are asked to multiply and simplify this expression if necessary.

STEP 2

We can simplify this expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c a(b + c) = ab + a*c.
In this case, we distribute $x^{2}$ to each term inside the parentheses.

STEP 3

Multiply $3 x^{2}$ with each term inside the parentheses.
$3 x^{2} 9 x^{5} -3 x^{2} x^{2} +3 x^{2} *5$

STEP 4

implify each term.
The multiplication of two exponents with the same base (in this case, x) can be simplified by adding the exponents.So, $x^{2} * x^{} = x^{2+} = x^{7}$

STEP 5

Apply the simplification to each term.
$27 x^{7} -12 x^{4} +15 x^{2}$ This is the simplified form of the given expression.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMultiply and simplify: 3x2(9x5−4x2+5)3 x^{2}(9 x^{5}-4 x^{2}+5)3x2(9x5−4x2+5)

Studdy Solution

STEP 1

Assumptions1. We are given the expression 3x(9x5−4x+5)3 x^{}\left(9 x^{5}-4 x^{}+5\right)3x(9x5−4x+5). We are asked to multiply and simplify this expression if necessary.

STEP 2

We can simplify this expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c a*(b + c) = a*b + a*c.In this case, we distribute x2 x^{2}x2 to each term inside the parentheses.

STEP 3

Multiply 3x23 x^{2}3x2 with each term inside the parentheses.3x2∗9x5−3x2∗x2+3x2∗53 x^{2} *9 x^{5} -3 x^{2} * x^{2} +3 x^{2} *53x2∗9x5−3x2∗x2+3x2∗5

STEP 4

implify each term.The multiplication of two exponents with the same base (in this case, x) can be simplified by adding the exponents.So, x2∗x=x2+=x7x^{2} * x^{} = x^{2+} = x^{7}x2∗x=x2+=x7

STEP 5

Apply the simplification to each term.27x7−12x4+15x227 x^{7} -12 x^{4} +15 x^{2}27x7−12x4+15x2This is the simplified form of the given expression.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMultiply and simplify: $3 x^{2}(9 x^{5}-4 x^{2}+5)$

Assumptions1. We are given the expression $3 x^{}\left(9 x^{5}-4 x^{}+5\right)$ . We are asked to multiply and simplify this expression if necessary.

We can simplify this expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c a(b + c) = ab + a*c.
In this case, we distribute $x^{2}$ to each term inside the parentheses.

Multiply $3 x^{2}$ with each term inside the parentheses.
$3 x^{2} 9 x^{5} -3 x^{2} x^{2} +3 x^{2} *5$

implify each term.
The multiplication of two exponents with the same base (in this case, x) can be simplified by adding the exponents.So, $x^{2} * x^{} = x^{2+} = x^{7}$

Apply the simplification to each term.
$27 x^{7} -12 x^{4} +15 x^{2}$ This is the simplified form of the given expression.