Question

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

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Solution

Step 1: Find the product of (3x+4) (3x-5) using a suitable identity.$\left(3\mathrm{x}+4\right)\left(3\mathrm{x}-5\right)$ is given.We can simply find the product of $\left(3x+4\right)\left(3x-5\right)$ by using the following identity: $\mathbf{\left(}\mathbf{x}\mathbf{+}\mathbf{a}\mathbf{\right)}\mathbf{\left(}\mathbf{x}\mathbf{+}\mathbf{b}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\mathbf{x}\mathbf{²}\mathbf{+}\mathbf{\left(}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{\right)}\mathbf{x}\mathbf{+}\mathbf{ab}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{*}\mathbf{\right)}$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+\left(4-5\right)3\mathrm{x}+\left(4\right)\left(-5\right)$$=9\mathrm{x}²+\left(-1\right)\left(3\mathrm{x}\right)-20$$=9x²-3x-20$Hence, the product of$\mathbf{}\mathbf{\left(}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{\right)}\mathbf{}\mathbf{\left(}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{5}\mathbf{\right)}\mathbf{}$using a suitable identity is $\mathbf{9}\mathbf{x}\mathbf{²}\mathbf{}\mathbf{-}\mathbf{3}\mathbf{x}\mathbf{}\mathbf{-}\mathbf{20}\mathbf{.}$

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