multiplying a binomial by a trinomial

drag each tile to the table to multiply each row heading by each column heading.

tiles:
$2d^3$, $-4d$, $-99d$, $11d^2$, $-18d^2$, $36$

table:
| | $2d^2$ | $11d$ | $-4$ |
|---|---|---|---|
| $d$ | | | |
| $-9$ | | | |

Question

multiplying a binomial by a trinomial

drag each tile to the table to multiply each row heading by each column heading.

tiles:
$2d^3$, $-4d$, $-99d$, $11d^2$, $-18d^2$, $36$

table:
| | $2d^2$ | $11d$ | $-4$ |
|---|---|---|---|
| $d$ | | | |
| $-9$ | | | |

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Area Model Multiplication" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Area Model Multiplication" ] } ## Multiply first row elements $$ \begin{aligned} &d \cdot 2d^2 = 2d^3\ &d \cdot 11d = 11d^2\ &d \cdot (-4) = -4d \end{aligned} $$ ## Multiply second row elements $$ \begin{aligned} &-9 \cdot 2d^2 = -18d^2\ &-9 \cdot 11d = -99d\ &-9 \cdot (-4) = 36 \end{aligned} $$ ## Construct the final table $$ \begin{array}{|c|c|c|c|} \hline & 2d^2 & 11d & -4 \ \hline d & 2d^3 & 11d^2 & -4d \ \hline -9 & -18d^2 & -99d & 36 \ \hline \end{array} $$ | | $2d^2$ | $11d$ | $-4$ | |---|---|---|---| | **$d$** | $2d^3$ | $11d^2$ | $-4d$ | | **$-9$** | $-18d^2$ | $-99d$ | $36$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Multiply first row elements

Multiply second row elements

Construct the final table

Answer: