Find each product. (y^4+2 z)^2

Name: Problem 251, Chapter 5: Intermediate Algebra
Uploaded: 2022-09-28T22:52:51-08:00
Duration: 2 min 46 s
Channel: Brooke Bussoletti
Description: Find each product. (y^4+2 z)^2

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Square of a Binomial

This concept involves expanding an expression of the form (a + b)², which can be done using the identity (a + b)² = a² + 2ab + b². Understanding this technique allows one to quickly and accurately expand and simplify binomial expressions raised to the second power.

Distributive Property

The distributive property is a fundamental principle in algebra that enables the multiplication of a single term across terms inside a parenthesis, expressed as a(b + c) = ab + ac. This property is essential for expanding expressions and combining like terms during the process of multiplication.

Exponent Laws

Exponent laws are rules that govern the operations on expressions involving powers, such as multiplying like bases or raising a power to another power. These rules help in simplifying and manipulating expressions that involve exponents, ensuring that terms are correctly expanded and combined.

Transcript

0:00 All right.

00:01 In this equation, we have y to the fourth plus 2z squared.

00:06 What we need to learn right away is that when we have something squared, it means we're multiplying it by itself, whether that be a number, a variable, or in this case, a binomial.

00:17 So we can expand this binomial, and we actually need to in order to solve, so that we can see it is the same equation multiplied by itself.

00:29 Now we can do the method that i want to review.

00:32 When you have a binomial times a binomial, you can solve this by doing the foiling method, where f stands for first, o stands for outer, i stands for inner, and l stands for last.

00:51 First, the first terms in each sequence.

00:54 Why to the fourth times y to the fourth.

00:57 Now we need to recall the product rule of exponents.

01:00 When you're multiplying together terms that have exponents and like bases, the product rule says that you add together the exponents and keep the like base.

01:11 So this would be y to the 4 plus 4.

01:14 Y to the 8th.

01:17 O stands for outer, the outermost terms in each sequence.

01:21 First, the coefficients.

01:22 The coefficient in front of y to the 4th is 1, since there isn't 1 there.

01:27 So 1 times positive 2, positive 2...

Please give Ace some feedback