Question

( 4x^2+4х + 1) (Чx^2 - 4х +1)​

Answer 1

Given: 4x

2

+4x+1

=4x

2

+2x+2x+1, (split middle term so that resultant is same)

=(4x

2

+2x)+(2x+1), (group pair of terms)

=2x(2x+1)+1(2x+1), (factor each binomials)

=(2x+1)(2x+1), (factor out common factor (2x+1))

=(2x+1)

2

Aliter, use (a+b

2

)=a

2

+2ab+b

2

⇒4x

2

+4x+1=(2x)

2

+2×2x+1

2

=(2x+1)

2

Answer 2

Answer:

Solution:-

First write the given equation

$\qquad\quad {:}\longrightarrow\sf (4x^2+4x+1)(4x^2-4x+1)$

• Use distributive formula

${\boxed{\sf (a+b)(c+d)=a (c+d)+b (c+d)}}$

• Substitute the values

$\qquad\quad {:}\longrightarrow\sf 4x^2 (4x^2-4x+1)+4x(4x^2-4x+1)+1 (4x^2-4x+1)$

• Simplify

$\qquad\quad {:}\longrightarrow\sf 16x^4-16x^3+4x^2+16x^3-16x+4x+4x^2-4x+1$

• Together like polynomials

$\qquad\quad {:}\longrightarrow\sf 16x^4-16x^3+16x^3+4x^2+4x^2-16x+4x-4x+1$

• Add and subtract accordingly

$\qquad\quad {:}\longrightarrow\sf 16x^4+8x^2-16x+1$