Question

Find each product. $$ 3 t(4 t+1)^{2} $$

   Find each product.
$$
3 t(4 t+1)^{2}
$$

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 5, Problem 17

Instant Answer

Solved by Expert Brandon Fox

06/23/2020

Step 1

This can be done by squaring the first term, multiplying the terms together and doubling it, and then squaring the last term. So, we have: $$(4t+1)^{2} = (4t)^{2} + 2*(4t*1) + (1)^{2} = 16t^{2} + 8t + 1$$ Show more…

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Find each product. $$ 3 t(4 t+1)^{2} $$

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Key Concepts

Distributive Property

The distributive property is a fundamental algebraic rule used to multiply a term by each term inside a grouping symbol, such as a parenthesis. It allows us to break down and simplify multiplications involving sums, and it is key to expanding expressions where a monomial multiplies a polynomial.

Exponentiation of Binomials

Exponentiation of binomials involves raising a two-term expression to a power, often using well-known formulas like (a + b)² = a² + 2ab + b². This concept simplifies the process of expanding expressions when a binomial is squared or raised to any exponent.

Polynomial Multiplication

Polynomial multiplication is the process of multiplying each term in one polynomial by each term in another and then combining like terms to simplify the result. This technique generalizes the distributive property to more complex algebraic expressions.

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