Type The Correct Answer In Each Box. Use Numerals Instead Of Words. If Necessary, Use [I] For The Fraction Bar(s).Find The Missing Term And The Missing Coefficient. { (6a - \square)(a - 21) = 15a^2 - 35a$}$

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Introduction

Algebraic equations are a fundamental concept in mathematics, and solving them requires a deep understanding of various mathematical operations and techniques. In this article, we will focus on solving a specific type of algebraic equation, where we need to find the missing term and coefficient. We will use the given equation as an example and provide step-by-step solutions to find the missing term and coefficient.

The Given Equation

The given equation is:

(6a−□)(a−21)=15a2−35a{(6a - \square)(a - 21) = 15a^2 - 35a}

Step 1: Expand the Left-Hand Side of the Equation

To solve this equation, we need to expand the left-hand side using the distributive property. This will allow us to compare the coefficients of the terms on both sides of the equation.

(6a−□)(a−21)=6a(a−21)−□(a−21){(6a - \square)(a - 21) = 6a(a - 21) - \square(a - 21)}

Step 2: Simplify the Expression

Now, we can simplify the expression by multiplying the terms inside the parentheses.

6a(a−21)−□(a−21)=6a2−126a−□a+21□{6a(a - 21) - \square(a - 21) = 6a^2 - 126a - \square a + 21\square}

Step 3: Compare the Coefficients

We can now compare the coefficients of the terms on both sides of the equation. The coefficient of the a2a^2 term on the left-hand side is 6, and the coefficient of the a2a^2 term on the right-hand side is 15. Since the coefficients of the a2a^2 term are different, we need to find the missing term that will make the coefficients of the a2a^2 term equal.

Step 4: Find the Missing Term

To find the missing term, we need to set up an equation that equates the coefficients of the a2a^2 term on both sides of the equation.

6a2−□a+21□=15a2−35a{6a^2 - \square a + 21\square = 15a^2 - 35a}

We can now simplify the equation by combining like terms.

6a2−□a+21□=15a2−35a{6a^2 - \square a + 21\square = 15a^2 - 35a}

6a2−□a+21□−15a2=−35a{6a^2 - \square a + 21\square - 15a^2 = -35a}

−9a2−□a+21□=−35a{-9a^2 - \square a + 21\square = -35a}

Step 5: Find the Missing Coefficient

We can now find the missing coefficient by equating the coefficients of the aa term on both sides of the equation.

−9a2−□a+21□=−35a{-9a^2 - \square a + 21\square = -35a}

−□a+21□=−35a+9a2{-\square a + 21\square = -35a + 9a^2}

−□a+21□=−35a+9a2{-\square a + 21\square = -35a + 9a^2}

−□a+21□+35a=9a2{-\square a + 21\square + 35a = 9a^2}

−□a+35a+21□=9a2{-\square a + 35a + 21\square = 9a^2}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

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−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

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−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

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−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

Q&A: Solving Algebraic Equations

Q: What is the first step in solving an algebraic equation? A: The first step in solving an algebraic equation is to expand the left-hand side of the equation using the distributive property.

Q: How do I simplify the expression after expanding the left-hand side? A: To simplify the expression, you need to multiply the terms inside the parentheses and combine like terms.

Q: What is the next step after simplifying the expression? A: The next step is to compare the coefficients of the terms on both sides of the equation.

Q: How do I find the missing term in the equation? A: To find the missing term, you need to set up an equation that equates the coefficients of the terms on both sides of the equation.

Q: What is the final step in solving the equation? A: The final step is to solve for the missing term and coefficient.

Q: Can you provide an example of how to solve an algebraic equation? A: Let's use the equation:

[(6a - \square)(a - 21) = 15a^2 - 35a}$

To solve this equation, we need to expand the left-hand side using the distributive property.

(6a−□)(a−21)=6a(a−21)−□(a−21){(6a - \square)(a - 21) = 6a(a - 21) - \square(a - 21)}

Next, we simplify the expression by multiplying the terms inside the parentheses.

6a(a−21)−□(a−21)=6a2−126a−□a+21□{6a(a - 21) - \square(a - 21) = 6a^2 - 126a - \square a + 21\square}

Now, we compare the coefficients of the terms on both sides of the equation.

6a2−126a−□a+21□=15a2−35a{6a^2 - 126a - \square a + 21\square = 15a^2 - 35a}

We can now find the missing term by setting up an equation that equates the coefficients of the terms on both sides of the equation.

6a2−126a−□a+21□=15a2−35a{6a^2 - 126a - \square a + 21\square = 15a^2 - 35a}

6a2−126a−□a+21□−15a2=−35a{6a^2 - 126a - \square a + 21\square - 15a^2 = -35a}

−9a2−□a+21□=−35a{-9a^2 - \square a + 21\square = -35a}

Finally, we solve for the missing term and coefficient.

−□a+21□=−35a+9a2{-\square a + 21\square = -35a + 9a^2}

−□a+21□+35a=9a2{-\square a + 21\square + 35a = 9a^2}

−□a+35a+21□=9a2{-\square a + 35a + 21\square = 9a^2}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

−□a+35a+21□−9a2=0{-\square a + 35a + 21\square - 9a^2 = 0}

Q: What is the missing term in the equation? A: The missing term is â–¡a\square a.

Q: What is the missing coefficient in the equation? A: The missing coefficient is 42.

Q: Can you provide another example of how to solve an algebraic equation? A: Let's use the equation:

(3x+2)(x+5)=9x2+27x+10{(3x + 2)(x + 5) = 9x^2 + 27x + 10}

To solve this equation, we need to expand the left-hand side using the distributive property.

(3x+2)(x+5)=3x(x+5)+2(x+5){(3x + 2)(x + 5) = 3x(x + 5) + 2(x + 5)}

Next, we simplify the expression by multiplying the terms inside the parentheses.

3x(x+5)+2(x+5)=3x2+15x+2x+10{3x(x + 5) + 2(x + 5) = 3x^2 + 15x + 2x + 10}

Now, we compare the coefficients of the terms on both sides of the equation.

3x2+15x+2x+10=9x2+27x+10{3x^2 + 15x + 2x + 10 = 9x^2 + 27x + 10}

We can now find the missing term by setting up an equation that equates the coefficients of the terms on both sides of the equation.

3x2+15x+2x+10=9x2+27x+10{3x^2 + 15x + 2x + 10 = 9x^2 + 27x + 10}

3x2+15x+2x+10−9x2=27x+10{3x^2 + 15x + 2x + 10 - 9x^2 = 27x + 10}

−6x2+17x+10=27x+10{-6x^2 + 17x + 10 = 27x + 10}

Finally, we solve for the missing term and coefficient.

−6x2+17x+10−27x=10{-6x^2 + 17x + 10 - 27x = 10}

−6x2−10x+10=10{-6x^2 - 10x + 10 = 10}

−6x2−10x=0{-6x^2 - 10x = 0}

−6x2=10x{-6x^2 = 10x}

−6x2+10x=0{-6x^2 + 10x = 0}

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