Explications étape par étape:
8) T= x² + 8x +16
= x² + 2×x×4 + 4²
= (x+4)²
U= y² +2y +1
= y² + 2×y×1 + 1²
= (y+1)²
V= x² -14x +49
= x² - 2×x×7 + 7²
= (x-7)²
W= x² -16x +64
= x² - 2×x×8 + 8²
= (x-8)²
X= 4x² - 49
= (2x)² - 7²
= (2x -7)(2x +7)
Y= 100 -9y²
= 10² - (3y)²
= (10 - 3y)(10 + 3y)
Z= (2x +1)² - 64
= (2x +1)² - 8²
= (2x +1 -8)(2x +1 +8)
= (2x -7)(2x +9)
9) 1) A= (4x -3)² - (3x +1)(4x -3)
= [(4x)² - 2×4x×3 + 3²] - [3x×4x - 3x×3 + 1×4x - 1×3]
= (16x² -24x +9) - (12x² - 9x + 4x - 3)
= (16x² -24x +9) - (12x² -5x -3)
= 16x² -24x +9 -12x² +5x +3
= 16x² -12x² -24x +5x +9 +3
= 4x² -19x +12
2) A= (4x -3)² - (3x +1)(4x -3)
= (4x -3) [(4x -3) - (3x +1)]
= (4x -3) (4x -3 -3x -1)
= (4x -3)(x -4)
3) A= (4x -3)² - (3x +1)(4x -3)
= (4×0 -3)² - (3×0 +1)(4×0 -3)
= (0-3)² - (0+1)(0-3)
= (-3)² - 1 × (-3)
= 9 +3
= 12
4) A= (4x -3)² - (3x +1)(4x -3)
= (4×4 -3)² - (3×4 +1)(4×4 -3)
= (16 -3)² - (12+1)(16-3)
= 13² - (13×13)
= 169 - 169
= 0
