Expand (2x-3)×(5x-7): Complete Binomial Multiplication

(2x3)×(5x7) (2x-3)\times(5x-7)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:05 Let's open parentheses properly, multiply each factor by each factor
00:30 Let's calculate the products
00:53 Let's collect the terms
01:01 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(2x3)×(5x7) (2x-3)\times(5x-7)

2

Step-by-step solution

To answer this exercise, we need to understand how the extended distributive property works:

For example:

(a+1)∗(b+2)

To solve this type of exercises, the following steps must be taken:

Step 1: multiply the first factor of the first parentheses by each of the factors of the second parentheses.

Step 2: multiply the second factor of the first parentheses by each of the factors of the second parentheses.

Step 3: group like terms together.

ab∗2ab∗2

We start from the first number of the exercise: 2x

2x*5x+2x*-7

10x²-14x

We will continue with the second factor: -3

-3*5x+-3*-7

-15x+21

We add all the data together:

10x²-14x-15x+21

10x²-29x+21

3

Final Answer

10x229x+21 10x^2-29x+21

Practice Quiz

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\( (3+20)\times(12+4)= \)

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