Visualisation of Factorisation

Q. Find the following product:

$\left(iv\right)$ $(3x-4y+5z)(9x^2+16y^2+25z^2+12xy-$

$15zx+20yz)$

Q.

Which of the following identity is not applicable to simplify ${(4x+5y)}^2$ - ${(5x+4y)}^2$?

1. = + 2ab +

2. - = (a + b)(a - b)

3. = - 2ab +

4. Both A and B

Q.

Find the area of the rectangle whose sides are : $40\text{cm}$ and $20\text{cm}$

Q.

The length of a rectangle is $3m$ and breadth $400cm$.

Find its perimeter.

Q. Use a suitable identity to get each of the following products:
$(\frac{x}{2}+\frac{3y}{4})(\frac{x}{2}+\frac{3y}{4})$

1. $\frac{x^2}{4}+\frac{3}{4}xy+\frac{9}{16}{y}^2$
2. $\frac{x^2}{2}+\frac{3}{2}xy+\frac{9}{8}{y}^2$
3. $\frac{x^2}{4}+\frac{3}{2}xy+\frac{9}{16}{y}^2$
4. $\frac{x^2}{4}+\frac{3}{16}xy+\frac{3}{4}{y}^2$

Q. Simplify : (3x + 2y)(3x + 4y) =

1. 9x² + 15xy + 8y²
2. 9x² - 6xy - 8y²
3. 9x² + 5xy - 8y²

Q. Match the following expressions using suitable identities.

1. $(m-4{)}^2$
2. $(3m+2)(3m-2)$
3. $(m+2)(m+7)$

Q. If $a=24,b=26,c=28$, then the value of $a^2+b^2+c^2-ab-bc-ac$ will be

1. $4$
2. $12$
3. $8$
4. $0$