### Video Transcript

Find the value of the determinant of the matrix π plus π₯, five π, π plus seven π¦, negative seven π.

Remember, for a two-by-two matrix π΄ with elements π, π, π, π, its determinant can be found by subtracting the product of elements π and π from the product of elements π and π. In our matrix, the element π is given as π plus π₯. π is given as five π. π is π plus seven π¦. And π is negative seven π.

To find its determinant then, we need to find the product of π and π. Thatβs π plus π₯ multiplied by negative seven π. I inverted that as negative seven π multiplied by π plus π₯. Weβre then going to subtract the product of the elements in the top right and bottom left. Thatβs π and π. And weβre going to subtract five π multiplied by π plus seven π¦.

Weβll need to expand each of these brackets as normal. Negative seven π multiplied by π is negative seven ππ. And negative seven π multiplied by π₯ is negative seven ππ₯. Negative five π multiplied by π is negative five ππ. And negative five π multiplied by seven π¦ is negative 35ππ¦.

Finally, we need to simplify this expression by collecting like terms. Here, we have two terms that are some multiple of ππ. Negative seven ππ minus five ππ is negative 12ππ.

And therefore, the determinant of our matrix is negative seven ππ₯ minus 35ππ¦ minus 12ππ.