a) \(\left(3x+4\right)^2+\left(4x-1\right)^2+\left(2x+5\right)\left(2x-5\right)\)
\(=\left[\left(3x\right)^2+2\cdot3x\cdot4+4^2\right]+\left[\left(4x\right)^2-2\cdot4x\cdot1+1^2\right]+\left[\left(2x\right)^2-5^2\right]\)
\(=9x^2+24x+16+16x^2-8x+1+4x^2-25\)
\(=\left(9x^2+16x^2+4x^2\right)+\left(24x-8x\right)+\left(16+1-25\right)\)
\(=29x^2+16x-8\)
b) \(\left(2x+1\right)\left(4x^2-2x+1\right)+\left(2-3x\right)\left(4+6x+9x^2\right)\)
\(=\left[\left(2x\right)^3+1^3\right]+\left[2^3-\left(3x\right)^3\right]\)
\(=8x^3+1+8-27x^3\)
\(=-19x^3+9\)
a) (3x + 4)² + (4x - 1)² + (2x + 5)(2x - 5)
= 9x² + 24x + 16 + 16x² - 8x + 1 + 4x² - 25
= (9x² + 16x² + 4x²) + (24x - 8x) + (16 + 1 - 25)
= 29x² + 16x - 8
b) (2x + 1)(4x² - 2x + 1) + (2 - 3x)(4 + 6x + 9x²)
= (2x)³ + 1³ + 2³ - (3x)³
= 8x³ + 1 + 8 - 27x³
= -19x³ + 9
\(a,\left(3x+4\right)^2+\left(4x-1\right)^2+\left(2x+5\right)\left(2x-5\right)\\ =9x^2+24x+16+16x^2-8x+1+4x^2-25\\ =\left(9x^2+16x^2+4x^2\right)+\left(24x-8x\right)+\left(16+1-25\right)\\ =29x^2-16x-8\)
\(b,\left(2x+1\right)\left(4x^2-2x+1\right)+\left(2-3x\right)\left(4+6x+9x^2\right)\\ =8x^3-4x^2+2x+4x^2-2x+1+8+12x+18x^2-12x-18x^2-27x^3\\ =\left(8x^3-27x^3\right)+\left(4x^2+18x^2-18x^2-4x^2\right)+\left(2x-2x+12x-12\right)+\left(1+8\right)\\ =-19x^3+9\)
