Question

Find the product of the following binomials: 2 (x²-2) (x²+7)​

Answer 1

Step-by-step explanation:

2(x²-2)(x²+7)

(2x²-4)(x²+7)

2x²(x²+7)-4(x²+7)

2x⁴+14x²-4x²+28

2x⁴+10x²+28

Answer 2

Question:

Find the product of the following binomials: 2 (x²-2) (x²+7).

To find:

★ To find the value of the given expression.

Answer:

$\underline{ \: \underline{ \bold{ 2 {x}^{4} + 10 {x}^{2} - 28} } \: } \: is \: the \: answer.$

Given:

An expression is given,

$2( {x}^{2} - 2)( {x}^{2} + 7)$

Step-by-step explanation:

$\sf2( {x}^{2} - 2)( {x}^{2} + 7)$

$\implies 2 \big[ { ({x}^{2} )}^{2} + ( - 2 + 7){x}^{2} + (7)( - 2) \big]$

Here, we use the formula

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

a = -2 , b = 7

$\implies 2 \big[ {x}^{4} + 5 {x}^{2} - 14 \big]$

$\implies \boxed{ 2 {x}^{4} + 10 {x}^{2} - 28}$

$\therefore \underline{ \bold{ 2 {x}^{4} + 10 {x}^{2} - 28} } \: is \: the \: answer.$

Formula used:

$\bigstar{(x + a)(x + b) = {x}^{2} + (a + b)x + ab}$

Formula to know:

$\bigstar {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

$\bigstar {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$\bigstar {a}^{2} - { b}^{2} = (a + b)(a - b)$

$\bigstar {a}^{3} + { b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

$\bigstar {a}^{3} - { b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$