4A
a) VT = $\dfrac{(a+b)^2-(a-b)^2}{4}$
= $\dfrac{a^2+2ab+b^2-a^2+2ab-b^2}{4}$
= $\dfrac{4ab}{4}$
= ab = VP (đpcm)
b) VP = (x + y)² + (x - y)²
= x² + 2xy + y² + x² - 2xy + y²
= 2x² + 2y²
= 2(x² + y²) = VT (đpcm)
4B
a) VP = (x + y)² - 2xy
= x² + 2xy + y² - 2xy
= x² + y² = VT (đpcm)
b) VT = (a + b)² - (a - b)(a + b)
= a² + 2ab + b² - (a² - b²)
= a² + 2ab + b² - a² + b²
= 2ab + 2b²
= 2b(a + b) = VP (đpcm)
5A
a) M = (2x + y)² - (y - 2x)²
= (2x + y)² - (2x - y)² (vì (A - B)² = (B - A)² ∀ A, B)
= (2x + y + 2x - y)(2x + y - 2x + y)
= 4x.2y
= 8xy
b) N = (3x + 2)² + 2(2 + 3x)(1 - 2y) + (2y - 1)²
= (2 + 3x)² + 2(2 + 3x)(1 - 2y) + (1 - 2y)²
= (2 + 3x + 1 - 2y)²
= (3x - 2y + 3)²
c) P = (x² + 2xy)² + 2(x² + 2xy)y² + y⁴
= (x² + 2xy + y²)^2
= [(x + y)²]²
= (x + y)⁴
5B
a) A = (x - y)² + 4xy
= x² - 2xy + y² + 4xy
= x² + 2xy + y²
= (x + y)²
b) B = (6x - 2)² + 4(3x - 1)(2 + y) + (y + 2)²
= [2(3x - 1)]² + 2.2(3x - 1).(y + 2) + (y + 2)²
= (6x - 2 + y + 2)²
= (6x + y)²
c) C = (x - y)² + 2(x² - y²) + (x + y)²
= (x - y)² + 2(x - y)(x + y) + (x + y)²
= (x - y + x + y)²
= (2x)²
= 4x²
