Question

L
Factorise the following expressions.
(1) a² + 8a + 16
(ii) p2 – 10 p + 25
(iv) 49y2 + 84yz + 362
(vi) 121b2 – 88bc + 16c2​

Answer 1

Answer:

1.

(a)^{2} + 2(a)(4) + (4)^{2} \\ a {}^{2} + 4 {}^{2) + 2 (a)(4)+

using identity x^{2} + y {}^{2} + 2xy = (x + y) {}^{2}

here x = a and y = 4

(a + 4) ^{2}

2.

$(p) {}^{2} - 2(p)(5) + (5) {}^{2} \\ p {}^{2} + (5) {}^{2} - 2(p)(5) \\ using \: identity \: x {}^{2} + y {}^{2} + 2xy = (x + y) {}^{2} \\ (p + 5) {}^{2}$

3.

$(7y) {}^{2} + 2(7y)(6z) + (6z) {}^{2} \\ (7y) {}^{2} +(6z) {}^{2} + 2(7y)(6z) \\ using \: identity \: x {}^{2} + y {}^{2} + 2xy = (x + y) {}^{2} \\ (7y+ 6z) {}^{2}$

4.

$(11b) {}^{2} + 2(11b)(4c) + (4c) {}^{2} \\ (11b )^{2} + (4c) {}^{2} + 2(11b)(4c) \\ using \: identity \: x {}^{2} + y {}^{2} + 2xy = (x + y) {}^{2} \\ (11b + 4c) {}^{2}$

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Answer 2

square is denoted as ^2.

1). a^2+8a+16

a^2+4a+4a+16

a(a+4)+4(a+4)

(a+4)(a+4)

2). p^2–10p+25

P^2-5P-5p+25

p(p-5)-5(p-5)

(p-5)(p-5)

3). 49y^2-84yz+362

7y^2+2(7y)(6z)+6z^2

(7y^2)+(6z^2)+2(7y)(6z)

identity = x^2+y^2+2xy = (x+y)^2

(7y+6z)^2

4). 121b^2-88bc+16c^2

(11b)^2+2(11b)(4c)+(4c)^2

11(b)^2+4c^2+2(11b)(4c)

identity = x^2+y^2+2xy = ( x+y )^2

(11b+4c)^2