Distribute First Term: Distribute the first term of the first binomial across the second binomial. We need to multiply 3x by each term in the second binomial (19x + 12). 3x * 19x = 57x^2 (Multiplying the x terms) 3x * 12 = 36x (Multiplying x by the constant) So, we have 57x^2 + 36x after this step.Distribute Second Term: Distribute the second term of the first binomial across the second binomial. Now we multiply 27 by each term in the second binomial (19x + 12). 27 * 19x = 513x (Multiplying the constant by the x term) 27 * 12 = 324 (Multiplying the constants) So, we have 513x + 324 after this step.Combine Results: Combine the results from Step 1 and Step 2. We add the expressions we found in the previous steps together. (57x^2 + 36x) + (513x + 324)Combine Like Terms: Combine like terms. We add the x terms together. 57x^2 + (36x + 513x) + 324 57x^2 + 549x + 324

Algebra 1

Add and subtract polynomials

Full solution

(3x+27)(19x+12)

Distribute First Term: Distribute the first term of the first binomial across the second binomial. $\newline$ We need to multiply $3x$ by each term in the second binomial ( $19x + 12$ ). $\newline$ $3x \times 19x = 57x^2$ (Multiplying the x terms) $\newline$ $3x \times 12 = 36x$ (Multiplying x by the constant) $\newline$ So, we have $57x^2 + 36x$ after this step.
Distribute Second Term: Distribute the second term of the first binomial across the second binomial. $\newline$ Now we multiply $27$ by each term in the second binomial ( $19x + 12$ ). $\newline$ $27 \times 19x = 513x$ (Multiplying the constant by the x term) $\newline$ $27 \times 12 = 324$ (Multiplying the constants) $\newline$ So, we have $513x + 324$ after this step.
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ We add the expressions we found in the previous steps together. $\newline$ $(57x^2 + 36x) + (513x + 324)$
Combine Like Terms: Combine like terms. $\newline$ We add the $x$ terms together. $\newline$ $57x^2 + (36x + 513x) + 324$ $\newline$ $57x^2 + 549x + 324$