need help with this other question ### Mathematical Expression for Educational ContentThe given mathematical expression is:\[ 2a \left( 7a^2b^2 + ab^2 + 5b \right) - 9b \left( -2a^2b^2 + 2b^2 + 3a \right) \]This expression involves two main components:1. The first term inside the parentheses, $2a (7a^2b^2 + ab^2 + 5b)$, where: - $7a^2b^2$ is a term involving both $a$ and $b$ raised to powers of 2. - $ab^2$ is a product of $a$ and $b$, with $b$ raised to the power of 2. - $5b$ is a linear term in $b$.2. The second term inside the parentheses, $-9b (-2a^2b^2 + 2b^2 + 3a)$, where: - $-2a^2b^2$ includes a negative sign and involves both $a$ and $b$ raised to powers of 2. - $2b^2$ is a quadratic term in $b$. - $3a$ is a linear term in $a$. #### Detailed Breakdown:- **First Parenthesis**: Multiply $2a$ by each term inside the parenthesis: \[ 2a \left( 7a^2b^2 + ab^2 + 5b \right) = (2a)(7a^2b^2) + (2a)(ab^2) + (2a)(5b) = 14a^3b^2 + 2a^2b^2 + 10ab \] - **Second Parenthesis**: Multiply $-9b$ by each term inside the parenthesis: \[ -9b \left( -2a^2b^2 + 2b^2 + 3a \right) = (-9b)(-2a^2b^2) + (-9b)(2b^2) + (-9b)(3a) = 18a^2b^3 - The given mathematical expression is:\[ -4d (5d^2 - 12) + 7 (d + 5) \]This expression involves the variable $ d $ and includes terms with different degrees of $ d $. It demonstrates polynomial multiplication and addition. The operations need to be carried out as follows:1. First, distribute $-4d$ through the polynomial $5d^2 - 12$.2. Second, distribute $7$ through the polynomial $d + 5$.Breaking it down step-by-step:\[ -4d \cdot 5d^2 - (-4d) \cdot 12 + 7 \cdot d + 7 \cdot 5 \]This leads to:\[ -20d^3 + 48d + 7d + 35 \]Combining like terms results in:\[ -20d^3 + 55d + 35 \]This is the simplified form of the given expression. Understanding these steps helps in mastering polynomial operations, which are fundamental in algebra.

Answered: – 4d (5ď² – 12) + 7 (d + 5)

Math

Algebra

– 4d (5ď² – 12) + 7 (d + 5)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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