Question

Q.24] Use suitable identity to find the product of (x+4) (x+10)​

Answer 1

Given:

• $\mathtt{(x + 4) \: (x + 10)}$

To Find:

• $\mathtt{Product \: of \: (x + 4) \: (x + 10)}$

Identity Used:

• $\mathtt{(x + a) \: (x + b) = {x}^{2} + (a + b) \: x + ab}$

Solution:

Here,

• $\mathtt{a = 4}$

• $\mathtt{b = 10}$

$\sf\underline{\bigstar\:According \: to \: question \: now \::} \\ \\ :\implies\mathrm{x(x + 10) + 4(x + 10)} \\ \\ :\implies\mathrm{ {x}^{2} + 10x + 4x + 40} \\ \\ :\implies{\underline{\boxed{\rm{ {x}^{2} + 14x + 40}}}}$

Thus,

$\therefore\;{\underline{\sf{Product\;of\;identity\;is \: \bf{30\;cm}.}}}$

Answer 2

$\large{\underline{\underline{\sf{Step\:by\:step\:explanation:}}}}$

Here we are asked to find the product of (x+4)(x+10) by using suitable identity.

To do so, we have to use this algebraic identity

:$\implies{\boxed{\tt{(x+a)(x+b)=\:x^{2}+(a+b)x +ab}}}$

_______

• Here, a = 4 and b = 10

:$\implies{\sf{x^{2}+(4+10)x+4\times10}}$

:$\implies{\sf{x^{2}+(14)x+40}}$

:$\large\implies{\boxed{\sf{\red{x^{2}+14x+40}}}}$

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