Question

$(3\mathrm{x}+4)(3\mathrm{x}-5)$ how to do it by using identities?

Answer 1

Step 1: Find the product of (3x+4) (3x-5) using a suitable identity.

$(3\mathrm{x}+4)(3\mathrm{x}-5)$ is given.

We can simply find the product of $(3x+4)(3x-5)$ by using the following identity:

$\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{a}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{b}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathbf{x}\mathbf{²}\mathbf{+}\mathbf{(}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{)}\mathbf{x}\mathbf{+}\mathbf{ab}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{*}\mathbf{)}$

Where $\mathbf{x}\mathbf{}\mathbf{\to }\mathbf{}\mathbf{3}\mathbf{x}\mathbf{,}\mathbf{}\mathbf{a}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathbf{,}\mathbf{}\mathbf{b}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{5}$

Using the above-given values in (*), we get

$=\left(3\mathrm{x}\right)²+(4-5)3\mathrm{x}+\left(4\right)(-5)$

$=9\mathrm{x}²+(-1)\left(3\mathrm{x}\right)-20$

$=9x²-3x-20$

Hence, the product of$\mathbf{}\mathbf{(}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{)}\mathbf{}\mathbf{(}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{5}\mathbf{)}\mathbf{}$using a suitable identity is $\mathbf{9}\mathbf{x}\mathbf{²}\mathbf{}\mathbf{-}\mathbf{3}\mathbf{x}\mathbf{}\mathbf{-}\mathbf{20}\mathbf{.}$