Squaring a binomial | Quadratics and polynomials | Algebra Basics | Khan Academy

TL;DR

To simplify (7x + 10)^2, multiply each term of the expression by itself and distribute accordingly.

Transcript

We're asked to simplify 7x plus 10 squared. And your temptation when you see something like this might be to just make it 7x squared plus 10 squared and that would be incorrect. Remember, when you're squaring something, you're multiplying something by itself. So this wouldn't be 7x squared plus 10 squared. This is equal to 7x plus 10 times 7x plus ... Read More

Key Insights

• 😑 Squaring an expression requires distributing the terms within the expression.
• 🍉 The simplified form of (7x + 10)^2 is obtained by multiplying each term within the expression by itself and then distributing the terms.
• 😑 The product of the two terms within the expression is repeated twice in the simplified form.

Questions & Answers

Q: Why can't we just square each term individually in (7x + 10)^2?

Squaring an expression means multiplying it by itself, so (7x + 10)^2 is not equivalent to 7x^2 + 10^2. It should be distributed as (7x + 10) * (7x + 10).

Q: Can we simplify (7x + 10)^2 to 7x^2 + 10^2?

No, that would be incorrect. The correct way to simplify (7x + 10)^2 is to distribute the terms and then multiply each term by itself.

Q: What is the simplified form of (7x + 10)^2?

The simplified expression is 49x^2 + 140x + 100. This is obtained by multiplying each term within the expression by itself and distributing accordingly.

Q: How can we quickly square a binomial like (7x + 10)^2?

A quick way to square a binomial like (7x + 10)^2 is to square the first term (49x^2), multiply the product of both terms by 2 (140x), and square the second term (100).

Summary & Key Takeaways

• When squaring an expression, such as (7x + 10)^2, do not simply square each term individually.

• Instead, distribute the expression, resulting in (7x + 10) * (7x + 10).

• Multiply each term within the expression by itself and distribute the terms again.

• The simplified expression is 49x^2 + 140x + 100.