Find the expansion geometrically: $(2 m + 1) (2 m + 9)$ .

Open in App

Solution

Step 1: Draw a square and cut into $4$ parts.
Step 2: There are $4$ rectangle and $1$ square.
Step 3: Area of the full rectangle, $A B C D =$ $(2 m + 9) (2 m + 1)$
Step 4: Now we have to find the area of inside square and rectangle as shown in the figure.
Step 5: Consider the area of pink square $=$ $(2 m)^{2}$ and the area of yellow rectangle $=$ length $\times$ breadth $=$ $18 m$
Step 6: Area of blue rectangle $=$ $2 m$ and the area of green rectangle $=$ $9$
Step 7: Area of full rectangle $=$ area of pink square $+$ area of yellow rectangle $+$ area of blue rectangle $+$ area of green rectangle.
i.e., $(2 m + 9) (2 m + 1) = (2 m)^{2} + 18 m + 2 m + 9$
$(2 m + 9) (2 m + 1) = (2 m)^{2} + m (18 + 2) + 9$
Hence, geometrically we expanded the identity $(2 m + 9) (2 m + 1) = (2 m)^{2} + m (18 + 2) + 9$ .

Suggest Corrections

Similar questions

(2 m + n^{2} + l)^{2}

(3 x + 2 y + z)^{2}

(2 x^{2} + x + 1)^{2}

(x + 5) (x + 6)

Join BYJU'S Learning Program